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  #1  
Old 04-08-2009, 07:43 PM
jakesteele jakesteele is offline
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Blackjack - average value per hand

I have worked in the casino biz for yrs. and one question I've always wondered is this: What is each hand worth, on average, win or loose, to the House?

If you have six players at a table all with $10 bets and the dealer wins, the House doesn't get $60 in profits. Same as if the House looses, it doesn't loose $60. If you average out over a year how many hands of blackjack are dealt divided by the amount of money taken in, or something like that.


Here are the initial figures I'm trying to work with.

Number of hands dealt

1. 6 hrs. of actual dealing time on table per day
2. 400 hands per hr. dealt
3. 2,400 hands dealt daily
4. 1,200 hands dealt weekly
5. 600,000 hands dealt yearly (50 wks)


Amounts of money on table

6. 6 spots @ $10 per hand ($60 per hand on table)
7. $27,000 in play hourly
8. $162,000 in play per 6 hr. work day
9. (my calculator doesn't go high enough to calculate yearly money)

This figure does not include overhead. The usual 'hold' on a bj table is about 22%, meaning that for every $100 taken in the house keeps about $22

Any math/casino whiz's out there?
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  #2  
Old 04-08-2009, 08:13 PM
Rigamarole Rigamarole is offline
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If played perfectly, the house edge in Blackjack is supposedly around 1% so the expected value of a $10 bet would be $9.90. Of course, many people don't play perfectly.
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  #3  
Old 04-08-2009, 08:52 PM
Fantome Fantome is offline
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Quote:
Originally Posted by jakesteele View Post
If you have six players at a table all with $10 bets and the dealer wins, the House doesn't get $60 in profits.
Why not?


Quote:
Same as if the House looses, it doesn't loose $60.
Do you mean if the house busts? No, they don't necessarily lose $60 because some players may have busted and the house has taken that money before the house busted, but if you mean the house lost to every player, then what do you mean by saying the house didn't lose $60?

Quote:
Number of hands dealt

1. 6 hrs. of actual dealing time on table per day
2. 400 hands per hr. dealt
3. 2,400 hands dealt daily
4. 1,200 hands dealt weekly
5. 600,000 hands dealt yearly (50 wks)
Your fourth figure should be 16,800 (assuming the casino is open 7 days a week).

And assuming that, your fifth figure should be 840,000 (the casino is off 14 days a year?).

Assuming that everyone follows the basic strategy, the expected value for the house is 1%, and the average bet is $10, in one year the casino makes $84,000 per table.


Quote:
Originally Posted by jakesteele View Post
This figure does not include overhead. The usual 'hold' on a bj table is about 22%, meaning that for every $100 taken in the house keeps about $22
Really? In that case, the casino would take in $1,848,000 per table.
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  #4  
Old 04-08-2009, 09:05 PM
Fantome Fantome is offline
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Quote:
Originally Posted by jakesteele View Post
I have worked in the casino biz for yrs. and one question I've always wondered is this: What is each hand worth, on average, win or loose, to the House?

...


The usual 'hold' on a bj table is about 22%, meaning that for every $100 taken in the house keeps about $22

Any math/casino whiz's out there?
You answered your own question.
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  #5  
Old 04-09-2009, 01:35 AM
Cyberhwk Cyberhwk is offline
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I'm not the "gambling math expert" requested but I do work in the industry. Maybe someone more mathematically inclined can correct me if I've gone off course.
Quote:
Originally Posted by jakesteele View Post
Number of hands dealt

1. 6 hrs. of actual dealing time on table per day
2. 400 hands per hr. dealt
3. 2,400 hands dealt daily
4. 1,200 hands dealt weekly
5. 600,000 hands dealt yearly (50 wks)
This would be completely irrelevant to your question of "Average Value Per Hand."

Quote:
Amounts of money on table

6. 6 spots @ $10 per hand ($60 per hand on table)
7. $27,000 in play hourly
8. $162,000 in play per 6 hr. work day
9. (my calculator doesn't go high enough to calculate yearly money)
Simple: $60 * House Edge of 1% = $0.60 per hand. At a full table with $10 a spot.

Not all that impressive, huh? Until you realize that you repeat this 600,000 times a year and your table's "Expected Value" is $360,000 profit. FOR A SINGLE TABLE.

More things to consider:
  • Almost NOBODY plays perfectly. Some are better than others but realistically, the house probably has at least a 1.5%-2% edge on a table collectively.
  • Add on another 2-3% if there is considerable play on a bonus bet.

Quadruple the house edge and you quadruple the expected value. Now your table is "expecting" $1.44 million a year.

Quote:
This figure does not include overhead. The usual 'hold' on a bj table is about 22%, meaning that for every $100 taken in the house keeps about $22
And hold is what's important anyway. "Expected value" is important, but you can't deposit it into a bank account.

Last edited by Cyberhwk; 04-09-2009 at 01:37 AM..
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  #6  
Old 04-09-2009, 01:52 AM
Cyberhwk Cyberhwk is offline
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Quote:
Originally Posted by Fantome View Post
Really? In that case, the casino would take in $1,848,000 per table.
A 22% hold =/= 22% House Edge. It just means that for every $100 that goes into the table $88 gets cashed out.

It's hard to compare hold and expected value (though they're definitely related) because hold is a function of money dropped into the table and expected value is a function of the amount BET.
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  #7  
Old 04-09-2009, 10:31 AM
Quercus Quercus is offline
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So a hold of 22% means that an average person that sits down at the table with $100 in chips will leave with $88?
If so, then hold should just be the house edge (about 1% for perfect non-counting BJ play) times the average number of bets for each person (between when they sit down and when they leave). That is, assuming people don't vary bet sizes and always play correct strategy. Which is probably not a very good assumption
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  #8  
Old 04-09-2009, 11:03 AM
Turble Turble is offline
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While it possible to precisely calculate the House Advantage for blackjack for a skilled player the fact that most players are not skilled makes it irrelevant to the original question. Studies done on actual live casino play show the real number to be around 2%.

Figuring about 50 hands per player per hour means the average player loses about one bet per hour. This number holds up in actual practice and many casinos use the one average bet per hour figure to calculate the Expected Value of a player to the house.

One average bet per hour also gives a very good real life estimate for the EV of a typical craps player.
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  #9  
Old 04-09-2009, 11:15 AM
Pleonast Pleonast is offline
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Please don't confuse "profit" (the surplus money after all expenses are paid) with "revenue" (the entire income before expenses). The numbers being used in this thread so far all seem to be revenue.
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  #10  
Old 04-09-2009, 11:28 AM
Fantome Fantome is offline
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Quote:
Originally Posted by Cyberhwk View Post
A 22% hold =/= 22% House Edge. It just means that for every $100 that goes into the table $88 gets cashed out.
I realize that. Assuming everyone plays using the basic strategy at all times (of course this never happens, I used it for calculations just to have a number), then the house edge and the hold are the same.


Quote:
Originally Posted by Quercus View Post
So a hold of 22% means that an average person that sits down at the table with $100 in chips will leave with $88?
If so, then hold should just be the house edge (about 1% for perfect non-counting BJ play) times the average number of bets for each person (between when they sit down and when they leave). That is, assuming people don't vary bet sizes and always play correct strategy. Which is probably not a very good assumption
It doesn't mater if they vary their betting size. The way you just calculated the hold is incorrect. Hold is calculated simply by comparing how much was bet over time and how much ended up going to the house. It has nothing to do with perfect play.
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  #11  
Old 04-09-2009, 11:34 AM
Fantome Fantome is offline
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Quote:
Originally Posted by Turble View Post
While it possible to precisely calculate the House Advantage for blackjack for a skilled player the fact that most players are not skilled makes it irrelevant to the original question. Studies done on actual live casino play show the real number to be around 2%.
According to this, it was determined in the recent past the hold for blackjack in the casinos on the Gulf Coast was 14.58%. I doubt any casinos have such good players on average that they are only making 2%.
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  #12  
Old 04-09-2009, 12:29 PM
jakesteele jakesteele is offline
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Quote:
Originally Posted by Fantome View Post
According to this, it was determined in the recent past the hold for blackjack in the casinos on the Gulf Coast was 14.58%. I doubt any casinos have such good players on average that they are only making 2%.
I'm not sure of all the numbers, but let me rephrase what I'm looking for. Example, when I used to sell long distance I would figure out what the 'average' cost per call was by dividing the money of the bill by the number of calls. 60 calls in one hour/$6.00 ld charge is ($6 divided by 60 calls = .10 cost on average per call.)

I'm trying to determine what the 'average' worth of any particular hand is, win, loose or draw when factored in with all of the other hands dealt that year.
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  #13  
Old 04-09-2009, 01:00 PM
Turble Turble is offline
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RE: When the house loses six $10 bets it does not lose $60. Looking at it in the long run (which is what really matters), it loses the Theoretical Expectation … $60 x 0.02 … the rest is held in what is known as the Escrow Effect. After sufficient trials the Actual Win will approach the Theoretical Expectation very closely … but for any one given hand the actual outcome of the hand does not matter.

RE: Hold. House Advantage and Hold are not the same thing. Hold is defined as the amount of money dropped in the box that is retained by the house after the players have cashed out their remaining chips at the end of their play.

If a player buys $100 in chips and makes ten $10 bets and just happens to end up exactly at Expectation (which is impossible), he will lose $10 x 10 bets x 0.02 = $2. If he then cashes out, the Hold is 2%. Most players do not cash out at the point, however. They continue to play with the same money. If that player were to manage to not go broke beforehand and played 100 hands with his original buy-in he would (theoretically) lose $20 and that $20 would then be the Hold. In real life the actual hold is affected by luck … Actual Hold = Original Buy - (Theoretical Expectation x Bet Amount x Number of Bets) x Standard Deviation … but luck doesn't matter to the casino so long as the players keep playing the luck factor will be minimized.

I agree that a 22% is quite a high Hold for BJ these days but it might be the case in areas in which gambling is new and the players still quite unsophisticated. The average in Las Vegas is more in the area of 16 to 17% but years ago it was in the 22% range.

jakesteel: Your real answer is 2%. That is the best approximation you are going to find.

Last edited by Turble; 04-09-2009 at 01:02 PM.. Reason: Edited to reply to jakesteele
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  #14  
Old 04-09-2009, 01:15 PM
Fantome Fantome is offline
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Quote:
Originally Posted by jakesteele View Post
I'm not sure of all the numbers, but let me rephrase what I'm looking for. Example, when I used to sell long distance I would figure out what the 'average' cost per call was by dividing the money of the bill by the number of calls. 60 calls in one hour/$6.00 ld charge is ($6 divided by 60 calls = .10 cost on average per call.)

I'm trying to determine what the 'average' worth of any particular hand is, win, loose or draw when factored in with all of the other hands dealt that year.
Okay, we can do this using the numbers you gave in the OP, but the numbers don't seem realistic to me (average bet only $10? I haven't even seen a $10 table in quite some time). It also seems you're hypothetical casino is only open five days a week, but we'll use the numbers you supplied just to work out an example:

Average bet: $10
Casino hold: 22%

The average casino worth for a hand played is $10 x .22 = $2.20
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  #15  
Old 04-09-2009, 01:42 PM
Turble Turble is offline
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Fantome, you still aren't getting what Hold means in casino lingo.
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  #16  
Old 04-09-2009, 01:54 PM
Fantome Fantome is offline
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Quote:
Originally Posted by Turble View Post
RE: When the house loses six $10 bets it does not lose $60.
Yes, it does.

Quote:
If a player buys $100 in chips and makes ten $10 bets and just happens to end up exactly at Expectation (which is impossible), he will lose $10 x 10 bets x 0.02 = $2.
Where are you getting this 2% figure?

Quote:
If he then cashes out, the Hold is 2%. Most players do not cash out at the point, however. They continue to play with the same money. If that player were to manage to not go broke beforehand and played 100 hands with his original buy-in he would (theoretically) lose $20 and that $20 would then be the Hold. In real life the actual hold is affected by luck … Actual Hold = Original Buy - (Theoretical Expectation x Bet Amount x Number of Bets) x Standard Deviation … but luck doesn't matter to the casino so long as the players keep playing the luck factor will be minimized.
What? In one sentence you're saying the hold is affected by luck (whatever that is) and then you say luck doesn't matter to the casino? This makes no sense.

And where are you getting "as the players keep playing the luck factor will be minimized?" Are you talking about fatigue, sloppy play increasing, etc. or something else?


Quote:
The average in Las Vegas is more in the area of 16 to 17% but years ago it was in the 22% range.

...

jakesteel: Your real answer is 2%.
What?

Quote:
Fantome, you still aren't getting what Hold means in casino lingo.
What makes you say that?
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  #17  
Old 04-09-2009, 02:13 PM
pulykamell pulykamell is online now
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Quote:
Originally Posted by Fantome View Post
Yes, it does.
I agree. But I think Turble is figuring in long-term expections, which for a single trial, with the house losing 6 $10 bets, doesn't mean anything.

Quote:
Where are you getting this 2% figure?
I assume that's the house edge on blackjack, given perfect, or near-perfect play.


Quote:
And where are you getting "as the players keep playing the luck factor will be minimized?" Are you talking about fatigue, sloppy play increasing, etc. or something else?
Over the long run, with enough trials, any winning streak in players' luck will be minimalized and the house advantage will approach the expected numbers like 2% (or whatever).

At least that's what I think he's saying, although it's not really clearly worded.

As for Hold vs. House Advantage. I'm not sure what that means, either. Is hole house advantage minus overhead, or something else?

Last edited by pulykamell; 04-09-2009 at 02:14 PM..
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  #18  
Old 04-09-2009, 02:16 PM
Turble Turble is offline
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What makes me say that is: every Casino Management course and other gambling related course at UNLV, reading hundreds (perhaps thousands) of serious gambling related books, 22 years working in casinos, and 17 years earning a living as a professional gambler.

This is not meant as an insult or personal attack but you, sir, simply do not know what you are talking about. Your posts in this thread show that you do not understand Expected Value and therefore have no chance of understanding, much less explaining, its effect on Hold.

If you are interested, I suggest Getting the Best of It by David Sklansky as an excellent introduction to the subject.

Good luck.
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  #19  
Old 04-09-2009, 02:32 PM
Fantome Fantome is offline
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Quote:
Originally Posted by pulykamell View Post
As for Hold vs. House Advantage. I'm not sure what that means, either. Is hole house advantage minus overhead, or something else?
House advantage is the percentage the house would be expected to make if everyone played using the basic strategy, i.e. hit in this situation, double down in this one, etc. Hold is what is actually made due to players deviating from that strategy.

Quote:
I assume that's the house edge on blackjack, given perfect, or near-perfect play.
I thought so too, but he later said: "jakesteel: Your real answer is 2%. " I don't know which of the OP's questions he thinks he's answering.



Quote:
Originally Posted by Turble View Post
What makes me say that is: every Casino Management course and other gambling related course at UNLV, reading hundreds (perhaps thousands) of serious gambling related books, 22 years working in casinos, and 17 years earning a living as a professional gambler.

This is not meant as an insult or personal attack but you, sir, simply do not know what you are talking about. Your posts in this thread show that you do not understand Expected Value and therefore have no chance of understanding, much less explaining, its effect on Hold.

If you are interested, I suggest Getting the Best of It by David Sklansky as an excellent introduction to the subject.

Good luck.
Turble, the point of this message board is fighting ignorance. If I gave someone wrong information, don't just say "You're wrong; go read a book." What is it I said that was incorrect? And it would be nice if you responded to questions.
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  #20  
Old 04-09-2009, 03:20 PM
Turble Turble is offline
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“Where are you getting this 2% figure? “

Years ago a study was done in Atlantic City … they hired temporary workers to observe live games from the surveillance room and keep track of how the players actually played the hands. My years in the casino business confirm that this is a valid number. Nearly every casino rating system is based on it, though many of them aren't really aware of it … they simply do what has been proven to work.

“House advantage is the percentage the house would be expected to make if everyone played using the basic strategy, i.e. hit in this situation, double down in this one, etc.

You described only Theoretical House Advantage (EV) in the case in which all players play perfect Basic Strategy; it will be somewhere between +0.2% and about +2% depending on the house rules and number of decks . The EV of a player using an advanced strategy would be different, it would actually be negative. And the Actual Observed EV (which is the number that is meaningful in the real) world is about 2% from observation.

“Hold is what is actually made due to players deviating from that strategy. “

Hold has nothing to do with the players deviating from any strategy. I attempted to explain Hold previously but it is a confusing concept; perhaps you would read it again, although it actually has nothing to do with the original question posed by the OP and is really only of interest to casino executives.

“I thought so too, but he later said: 'jakesteel: Your real answer is 2%. ' I don't know which of the OP's questions he thinks he's answering.”

I am replying to “What is each hand worth, on average, win or loose, to the House? “. The answer to that question is: Approximately 2% of the bet. The other numbers and the mention of Hold by the OP are all pretty much red herrings and bear no relation to the actual question.

"You're wrong; go read a book."

The subject of Expected Value would require more time and effort than I am willing to expend right now; after all, entire books have been written about it. If you feel suggesting a book that will help fight your ignorance of the subject is not in the spirit of the board, perhaps you should start a new thread asking for an explanation of EV since the OP has been answered and your question is really a new one.

Fantome, I repeat, please don't take my posts as any sort of personal attack. We are dealing here with some very subtle distinctions in a very complex matter that very few people understand and I am doing my best to explain them in this limited format. Peace.
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  #21  
Old 04-09-2009, 03:50 PM
Fantome Fantome is offline
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Quote:
Originally Posted by Turble View Post
“Where are you getting this 2% figure? “

Years ago a study was done in Atlantic City … they hired temporary workers to observe live games from the surveillance room and keep track of how the players actually played the hands. My years in the casino business confirm that this is a valid number. Nearly every casino rating system is based on it, though many of them aren't really aware of it … they simply do what has been proven to work.
I'm not following you. What is this 2% supposed to reflect?

Quote:
“House advantage is the percentage the house would be expected to make if everyone played using the basic strategy, i.e. hit in this situation, double down in this one, etc.

You described only Theoretical House Advantage (EV) in the case in which all players play perfect Basic Strategy; it will be somewhere between +0.2% and about +2% depending on the house rules and number of decks .
Right. Why should I have described anything else? What did Ido wrong here in your eyes?


Quote:
The EV of a player using an advanced strategy would be different, it would actually be negative. And the Actual Observed EV (which is the number that is meaningful in the real) world is about 2% from observation.
Okay? You're bringing up strategies counting cards. How is this relevant to the thread? It seems that you're attempting to minimize something I wrote or claim I'm incorrect in some way because I didn't bring this up. Why?

Quote:
“Hold is what is actually made due to players deviating from that strategy. “

Hold has nothing to do with the players deviating from any strategy. I attempted to explain Hold previously but it is a confusing concept; perhaps you would read it again, although it actually has nothing to do with the original question posed by the OP and is really only of interest to casino executives.
Of course it has to do with deviating from basic strategy. If everyone played using the basic strategy, the hold would be x. The more that strategy is deviated from (and not because of card counting), the greater x becomes.

How do you figure the casino hold has nothing to do with the OP's question? It has everything to do with it. The OP wants to know how much the average worth for the casino a hand played is based on a 22% hold. How can the question be answered if we don't know how much the hold is for the casino?

Quote:
“I thought so too, but he later said: 'jakesteel: Your real answer is 2%. ' I don't know which of the OP's questions he thinks he's answering.”

I am replying to “What is each hand worth, on average, win or loose, to the House? “. The answer to that question is: Approximately 2% of the bet. The other numbers and the mention of Hold by the OP are all pretty much red herrings and bear no relation to the actual question.
You said, "I agree that a 22% is quite a high Hold for BJ these days but it might be the case in areas in which gambling is new and the players still quite unsophisticated. The average in Las Vegas is more in the area of 16 to 17% but years ago it was in the 22% range."

How can you then say the average worth of each hand to the house is only 2%?

Quote:
"You're wrong; go read a book."

The subject of Expected Value would require more time and effort than I am willing to expend right now; after all, entire books have been written about it. If you feel suggesting a book that will help fight your ignorance of the subject is not in the spirit of the board, perhaps you should start a new thread asking for an explanation of EV since the OP has been answered and your question is really a new one.
You said:
Quote:
Fantome, you still aren't getting what Hold means in casino lingo.
You never mentioned what it is I said that brought you to that conclusion. It's customary and expected to do that here. It doesn't mean writing an essay on Expected Value; it just requires you to point out what I said and maybe briefly describing why I don't understand what you claim I don't. I then asked, "What makes you say that? " Now I thought you might at least quote what it is I said that was incorrect. Do you? No. You respond by giving your credentials which included "reading hundreds (perhaps thousands) of serious gambling related books." Thousand of books on gambling? Really? Anyway, the point is one would think at that point you understood I wanted you to point out what it is I said that was incorrect.
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  #22  
Old 04-09-2009, 04:03 PM
Turble Turble is offline
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Originally Posted by Fantome View Post
... I wanted you to point out what it is I said that was incorrect.
/sigh
Everything.

I can't tell if you are a troll or simply dense.

/sigh
Uncle.
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  #23  
Old 04-09-2009, 04:19 PM
Colibri Colibri is online now
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Originally Posted by Turble View Post
/sigh
Everything.

I can't tell if you are a troll or simply dense.

/sigh
Uncle.
Moderator note

Turble, accusations of trolling are not permitted in GQ. Don't do this again.

Colibri
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  #24  
Old 04-09-2009, 04:42 PM
Turble Turble is offline
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Understood. I had tried to delete it but missed the edit window. Sorry.
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  #25  
Old 04-09-2009, 05:59 PM
Evil Economist Evil Economist is offline
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Suppose a player sits down at the Blackjack table with $100. He expects to lose about 2% a hand. That means that after playing 15 hands he has lost a total of $30, for a hold of 30%.

Even though the expected loss per hand is 2%, the dollar amount lost adds up over time. I believe that is the relationship between hold and EV.
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  #26  
Old 04-09-2009, 06:10 PM
pulykamell pulykamell is online now
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*nevermind*

Last edited by pulykamell; 04-09-2009 at 06:10 PM..
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  #27  
Old 04-09-2009, 06:37 PM
Fantome Fantome is offline
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Originally Posted by Evil Economist View Post
Suppose a player sits down at the Blackjack table with $100. He expects to lose about 2% a hand. That means that after playing 15 hands he has lost a total of $30, for a hold of 30%.
That's not how the hold is calculated. The hold is regarding how much of each bet the casino ends up with on average. It doesn't matter if the player sits down with $100 or $1,000; what matters is how much was bet and how much of it the casino kept.

You player sits down with $100, and makes 15 $100 bets for a total of $1,500 worth of bets. If he loses 2%- the hold is 2%; it's not 30% because his original bankroll was $100. What if he sat down with $200? Now the hold is $15%? No, the player's bankroll is irrelevant.
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  #28  
Old 04-09-2009, 06:57 PM
Turble Turble is offline
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First of all, understand that Hold is a red herring in regard to the original question. It is totally unrelated.

Let's define Hold as used by casinos … bear with me, this is all relevant to the question of “What is Hold?”

Players typically sit down at a table and make a buy-in, either for cash or for Table Credit (markers); they give the dealer cash or take a marker, the dealer gives them chips in return, and the dealer puts the cash in the drop box. The casino procedures for handling markers mean for our purposes we can simply consider them as cash to avoid unnecessary complications. A player may occasionally sit down who already has chips in hand; that will affect the Hold but only by an insignificantly small amount since it is so rare; we will ignore that effect in our calculations. We also ignore the rare occurrence of players who bet the cash (Money Plays) rather than exchange it for chips.

At the end of each shift all the drop boxes are removed from the tables and all the chips on the tables are counted … chips that were added or removed by the casino during the shift are accounted for … the cash is counted … the Hold is the amount of cash in the boxes plus or minus (sometimes the casino loses) the difference in the number of chips at the beginning of shift compared to the chip count at the end of the shift.

For example, if the Drop (total cash in the drop boxes) is $10,000 and there have been no chip transfers during the shift (just an accounting complication for our purpose) and the Count (the total number of chips on the tables) at the end of the shift is $8,000 less than it was at the beginning of the shift … then the Hold for that shift is $2,000. $10,000 cash That is the entire calculation for Casino Hold. Notice it has nothing to do with House Advantage or anything else.

What has been being discussed here is an attempt to calculate an estimation of what the Theoretical Hold should be … perhaps an interesting question but unrelated to the OP … in the real world, Hold is determined by an accounting procedure, not a calculation.
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  #29  
Old 04-09-2009, 07:11 PM
Evil Economist Evil Economist is offline
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Quote:
Originally Posted by Fantome View Post
That's not how the hold is calculated. The hold is regarding how much of each bet the casino ends up with on average. It doesn't matter if the player sits down with $100 or $1,000; what matters is how much was bet and how much of it the casino kept.

You player sits down with $100, and makes 15 $100 bets for a total of $1,500 worth of bets. If he loses 2%- the hold is 2%; it's not 30% because his original bankroll was $100. What if he sat down with $200? Now the hold is $15%? No, the player's bankroll is irrelevant.
Actually, I believe the bankroll does matter, which is why our definitions differ. They measure the difference between the chips you buy when you enter the casino and the chips you cash out when you exit the casino. If you buy $100 of chips and cash out $70 in chips, the hold is 30%.

Of course I may be wrong, so please feel free to cite me a source for your definition.

On edit, Turble said it better and more accurately than I did.

Last edited by Evil Economist; 04-09-2009 at 07:13 PM..
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  #30  
Old 04-09-2009, 07:35 PM
YamatoTwinkie YamatoTwinkie is offline
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Just to clarify, assuming basic strategy, if everyone that came to the table only played a single hand of Blackjack and then immediately cashed out (win or lose), the hold would only wind up being 2%, correct?

The discrepancy between the 2% (theoretical hold using the above example) and the ~20% figure comes in because people are generally more inclined to leave the table when they're down (ran out of chips, dealer is "cold", etc.) than up, right?
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  #31  
Old 04-09-2009, 07:50 PM
Evil Economist Evil Economist is offline
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Quote:
Originally Posted by YamatoTwinkie
Just to clarify, assuming basic strategy, if everyone that came to the table only played a single hand of Blackjack and then immediately cashed out (win or lose), the hold would only wind up being 2%, correct?
Yes, but not for the reasons you think; see below.

Quote:
The discrepancy between the 2% (theoretical hold using the above example) and the ~20% figure comes in because people are generally more inclined to leave the table when they're down (ran out of chips, dealer is "cold", etc.) than up, right?
Not exactly, the difference between the hold and the house edge is that you keep betting the same cash, losing 2% each time. Suppose you have $100 and you play some blackjack. In the first hand you play $100 and lose $2. That's a loss of 2% and a hold of 2%. Now suppose you play another hand. You play $98 (your remaining money) and lose approximately $2. You lost 2% again, but the casino now has $4 of your money and a hold percentage of 4%. If you play until you are out of money the casino will eventually have a hold of 100%, even though you lost no more than 2% each hand.

Note that you don't actually lose 2% each hand (you win some, you lose some, 2% is just the average result).

While checking the internet for cites on hold percentage, i found the following link:

Quote:
The house advantage - the all-important percentage that explains how casinos make money - is also called the house edge, the theoretical win percentage, and expected win percentage. In double-zero roulette, this figure is 5.3%. In the long run the house will retain 5.3% of the money wagered. In the short term, of course, the actual win percentage will differ from the theoretical win percentage (the magnitude of this deviation can be predicted from statistical theory). The actual win percentage is just the (actual) win divided by the handle. Because of the law of large numbers - or as some prefer to call it, the law of averages - as the number of trials gets larger, the actual win percentage should get closer to the theoretical win percentage.

Because handle can be difficult to measure for table games, performance is often measured by hold percentage (and sometimes erroneously called win percentage). Hold percentage is equal to win divided by drop. In Nevada, this figure is about 24% for roulette. The drop and hold percentage are affected by many factors; we won't delve into these nor the associated management issues. Suffice it to say that the casino will not in the long term keep 24% of the money bet on the spins of roulette wheel - well, an honest casino won't.
The link also gives the house edge for Blackjack at

Quote:
Blackjack average player 2.0%
Blackjack 6 decks, basic strategy 0.5%
Blackjack single deck, basic strategy 0.0%
Blackjack Card-Counting -1.00%
Blackjack Basic Strategy 0.50%
Blackjack Average player 2.00%
Blackjack Poor Player 4.00%

Last edited by Evil Economist; 04-09-2009 at 07:51 PM..
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  #32  
Old 04-09-2009, 08:02 PM
Fantome Fantome is offline
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Quote:
Originally Posted by Turble View Post
First of all, understand that Hold is a red herring in regard to the original question. It is totally unrelated.
No, it's not. The question was, "What is each hand worth, on average, win or loose, to the House?"

He then clarified in post #12:
"I'm trying to determine what the 'average' worth of any particular hand is, win, loose or draw when factored in with all of the other hands dealt that year."

I'll ask you again, since you didn't answer me the last time I asked (nor did you answer my other questions):
Quote:
How do you figure the casino hold has nothing to do with the OP's question? It has everything to do with it. The OP wants to know how much the average worth for the casino a hand played is based on a 22% hold. How can the question be answered if we don't know how much the hold is for the casino?
Now that you're back, are you going to answer any of my earlier questions? It would be nice if you answered all of my questions in post #22, especially since you said I was wrong about "everything." Was my answer in post #14 wrong that answered the OP's question after he clarified in post #12? I'd especially like to know how the answer to the OP's question is 2% and how a 2% figure was calculated by observing "live games from the surveillance room and keep track of how the players actually played the hands." What is that 2% supposed to represent? But it would be great if you answered all of them.




Quote:
Originally Posted by Evil Economist View Post
Actually, I believe the bankroll does matter, which is why our definitions differ. They measure the difference between the chips you buy when you enter the casino and the chips you cash out when you exit the casino. If you buy $100 of chips and cash out $70 in chips, the hold is 30%.

Of course I may be wrong, so please feel free to cite me a source for your definition.

On edit, Turble said it better and more accurately than I did.
I don't think it matters which way you define the word, as long as we agree with how things are calculated otherwise, which I think we do. On these matters, Turble and I don't agree and I'd like to see him address my questions.

Now, I don't see how the word "hold" can be defined differently then I'm defining it as I believe I'm defining it the way the OP intended, which is what's relevant:

Quote:
The usual 'hold' on a bj table is about 22%, meaning that for every $100 taken in the house keeps about $22
Quote:
I'm trying to determine what the 'average' worth of any particular hand is, win, loose or draw when factored in with all of the other hands dealt that year.
We couldn't calculate what he's asking us to if the 22% figure he supplied represents what amount of money was used to buy chips. We can calculate the answer for him if his definition of hold is the percentage of dollars bet that was kept by the casino since he's "trying to determine what the 'average' worth of any particular hand is, win, loose or draw when factored in with all of the other hands dealt that year."


Quote:
Originally Posted by YamatoTwinkie View Post
Just to clarify, assuming basic strategy, if everyone that came to the table only played a single hand of Blackjack and then immediately cashed out (win or lose), the hold would only wind up being 2%, correct?
Not if we're defining hold the way Evil Economist is. If a friend and I went to a blackjack table together and I bought in for $100 and he bought in for $10,000, and we then played one round, and each bet $100, lost and then cashed out, the casino's hold for me would be 100% and the casino's hold for him would be 1%.



Quote:
Originally Posted by YamatoTwinkie View Post
Just to clarify, assuming basic strategy, if everyone that came to the table only played a single hand of Blackjack and then immediately cashed out (win or lose), the hold would only wind up being 2%, correct?
Quote:
Originally Posted by Evil Economist View Post
Yes, but not for the reasons you think; see below.
That's not what you said.
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  #33  
Old 04-09-2009, 08:05 PM
Turble Turble is offline
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“Just to clarify, assuming basic strategy, if everyone that came to the table only played a single hand of Blackjack and then immediately cashed out (win or lose), the hold would only wind up being 2%, correct? “

Well, not exactly … well, almost … or, yes, if basic strategy for that particular table yields a 2% house advantage. The 2% figure I refer to is for the play of the general public (as observed in real life play) which is only an approximation of correct Basic Strategy … it contains several errors.

“The discrepancy between the 2% (theoretical hold using the above example) and the ~20% figure comes in because people are generally more inclined to leave the table when they're down (ran out of chips, dealer is "cold", etc.) than up, right? “

No. 2% is the House Advantage (more professionally, Expected Value [EV]). 20% is the Hold. They are not the same thing … see above.

People leaving when they are losing (or winning), cold (or hot) dealers, etc. have no effect on longterm hold … those things will all even out, or, more precisely, approach expectation. The reason a game with a house advantage of 2% can win 20% of the players' money is because the players bet the same money more than one time. That would open the can of worms known as Handle, a term we have not yet touched upon, as well as Win. Win (total dollars won by the house) is Handle (total amount bet by the players) x EV.

I told you guys it gets complicated; this is very esoteric stuff. If you look around a casino floor, the percentage of employees who can do these calculations is in the single digits, perhaps in the decimals.

Last edited by Turble; 04-09-2009 at 08:10 PM.. Reason: Evil Economist has it.
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  #34  
Old 04-09-2009, 08:24 PM
Evil Economist Evil Economist is offline
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Quote:
Originally Posted by Fantome
Quote:
Originally Posted by Turble
First of all, understand that Hold is a red herring in regard to the original question. It is totally unrelated.
No, it's not. The question was, "What is each hand worth, on average, win or loose, to the House?"
It's only related if you divide the hold by the number of hands played. you're better off looking at the house edge, which is 2%. See the cite in my last post, which links to a UNLV site that defines the terms and gives 2%. By the way, the OP needs to learn the difference between lose and loose.

Quote:
Originally Posted by Fantome
He then clarified in post #12:
"I'm trying to determine what the 'average' worth of any particular hand is, win, loose or draw when factored in with all of the other hands dealt that year."
The house edge would give him that number quite nicely. That's 2%.

Quote:
Originally Posted by Fantome
Quote:
Originally Posted by Evil Economist
Actually, I believe the bankroll does matter, which is why our definitions differ. They measure the difference between the chips you buy when you enter the casino and the chips you cash out when you exit the casino. If you buy $100 of chips and cash out $70 in chips, the hold is 30%.

Of course I may be wrong, so please feel free to cite me a source for your definition.

On edit, Turble said it better and more accurately than I did.
I don't think it matters which way you define the word, as long as we agree with how things are calculated otherwise, which I think we do. On these matters, Turble and I don't agree and I'd like to see him address my questions.
I think the definition of the word is all-important. Hold gives you the total losses. The OP wants the per-hand losses, which is a totally different number, and is about 2% of the bet.

Quote:
Originally Posted by Fantome
Now, I don't see how the word "hold" can be defined differently then I'm defining it as I believe I'm defining it the way the OP intended, which is what's relevant:
The UNLV webisite I linked to defined it the way I do, which is differently than you do. Do you have a different cite?


Quote:
Originally Posted by Fantome
Quote:
Originally Posted by YamatoTwinkie
Just to clarify, assuming basic strategy, if everyone that came to the table only played a single hand of Blackjack and then immediately cashed out (win or lose), the hold would only wind up being 2%, correct?
Not if we're defining hold the way Evil Economist is.
No, what I said was correct.

Quote:
Originally Posted by Fantome
If a friend and I went to a blackjack table together and I bought in for $100 and he bought in for $10,000, and we then played one round, and each bet $100, lost and then cashed out, the casino's hold for me would be 100% and the casino's hold for him would be 1%.
Yes, that's correct. And if you had lost $2 and he had lost $200 then you would have each lost 2% and the casino's hold would be 2%.

Quote:
Originally Posted by Fantome
Quote:
Originally Posted by YamatoTwinkie
Just to clarify, assuming basic strategy, if everyone that came to the table only played a single hand of Blackjack and then immediately cashed out (win or lose), the hold would only wind up being 2%, correct?
Quote:
Originally Posted by Evil Economist
Yes, but not for the reasons you think; see below.
That's not what you said.
Yes it is.

Take a moment and consider if you're correct, here. Search for cites that support your point of view. See if you can find any. Read Turble's post again. Read my cite. Is it possible you're operating from a mistaken assumption?
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  #35  
Old 04-09-2009, 08:35 PM
Turble Turble is offline
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By George, I think I've got it … the explanation, that is.

The original question was “What is each hand worth, on average, win or loose, to the House?”

I'll rephrase that in more professional language. What is the Expected Value of a hand of blackjack?

EV = House Advantage x $Amount of the Bet

Example: A game in which the House Advantage, for whatever reason, is 2% (given different rules or different players that number can vary.) A player wagers $10.

EV = 0.2 x $10
EV = 20 cents … in other words, that bet on that game is worth, on average, win or lose, 20 cents to the house … and that will hold true for any given House Advantage and any given $ amount bet.

Clear? Nothing else needed. That is the answer to that question.

PS: Good job, Evil. They're all yours for now; I gotta go.
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  #36  
Old 04-09-2009, 08:56 PM
Fantome Fantome is offline
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Quote:
Originally Posted by Evil Economist View Post
It's only related if you divide the hold by the number of hands played. you're better off looking at the house edge, which is 2%. See the cite in my last post, which links to a UNLV site that defines the terms and gives 2%.
The house edge is irrelevant to answering his question. What do you believe the answer to his question that he clarified in post #12 is and how did knowing the house edge help you arrive at it?


Quote:
By the way, the OP needs to learn the difference between lose and loose.
No, he doesn't. It's a common spelling mistake and that comment wasn't really necessary.

Quote:
The house edge would give him that number quite nicely. That's 2%.
No, it wouldn't, since we know the casinos make much more than that per hand and that's not the answer to the question the OP asked.


Quote:
I think the definition of the word is all-important. Hold gives you the total losses. The OP wants the per-hand losses, which is a totally different number, and is about 2% of the bet.
You believe the OP asked what the house edge is if everyone sticks to the basic strategy? That's not what he asked.

Quote:
The UNLV webisite I linked to defined it the way I do, which is differently than you do. Do you have a different cite?
I answered that what's relevant is the way the OP used the word and the question he asked can't be answered unless it's defined as the amount of money lost as compared to wagered.



Quote:
No, what I said was correct.
What? I said the answer to YamatoTwinkie's question is "no" if we're defining hold as you have.

Quote:
Yes it is.
No, it's not. YamatoTwinkie asked "Just to clarify, assuming basic strategy, if everyone that came to the table only played a single hand of Blackjack and then immediately cashed out (win or lose), the hold would only wind up being 2%, correct? "

You answered "yes".

The answer would be yes if we defined it as I have. The answer is unknown if defined as you have since we don't know how many chips each player bought when they sat at the table.



Quote:
Originally Posted by Turble View Post
The original question was “What is each hand worth, on average, win or loose, to the House?”

I'll rephrase that in more professional language. What is the Expected Value of a hand of blackjack?

EV = House Advantage x $Amount of the Bet
No, the house advantage would only be relevant in games like roulette where the house advantage is the same regardless of what "strategy" the player uses. In blackjack the house advantage assumes using basic strategy, which isn't even close to what the majority of players employ in real life.
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  #37  
Old 04-09-2009, 09:39 PM
Evil Economist Evil Economist is offline
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Quote:
Originally Posted by Fantome View Post
No, it wouldn't, since we know the casinos make much more than that per hand and that's not the answer to the question the OP asked.
Casinos don't make the hold percentage per hand. You are confusing the sum that casinos make over a bunch of hands (where players keep playing the same money over and over) with the amount they make per hand. By the way, this is the 10th time you've been told this. Does anyone else reading the thread have this same confusion, or is there only one person not getting it?

Quote:
You believe the OP asked what the house edge is if everyone sticks to the basic strategy? That's not what he asked.
He asked "What is each hand worth, on average, win or lose, to the House?"

Key concepts of this sentence are: each hand, and average.

And the answer is: the house makes on average 2% of the amount bet per hand. Using his numbers:

600,000 hands dealt yearly
6 spots at the table
$10 bets per spot.

Then the answer is that the house takes on average 2% ($0.20) per bet per spot (2% is the house edge of the average player--see the UNLV cite), for a total yearly take of 600,000*6*10*2%=$720,000. All sorts of assumptions there (e.g., the tables are always full, the house edge is 2%, etc.), but it's as good as we're likely to get without looking at real numbers. EDITED TO ADD: If 600,000 is the total number of hands dealt (not the numbers of hands per spot) then my numbers are off by a factor of 6, and the value would be 600,000*10*2%=120,000.

P.S., if the hold percentage is 22%, then we can also say that the average person plays about 6 hands.

Quote:
I answered that what's relevant is the way the OP used the word
Very good, except your answer was wrong.

Quote:
What? I said the answer to YamatoTwinkie's question is "no" if we're defining hold as you have.
The answer to YamatoTwinkie's question is "yes," if we define hold the way I have.

Quote:
No, it's not. YamatoTwinkie asked "Just to clarify, assuming basic strategy, if everyone that came to the table only played a single hand of Blackjack and then immediately cashed out (win or lose), the hold would only wind up being 2%, correct? "

You answered "yes".

The answer would be yes if we defined it as I have. The answer is unknown if defined as you have since we don't know how many chips each player bought when they sat at the table.
You are confused. It doesn't matter how much they bring to the table. If they only play one hand, and the house edge is 2%, then the hold is 2%. The fact that you think it matters how much money they bring to the table (if they only play one hand) makes me think you are misunderstanding something fundamental. (Remember, by the way, that the 2% is an average over thousands of players. you might lose $100 on a $100 bet, but the next guy may win $196 on a $100 bet).

Even if they play more than one hand, we can still come up with a theoretical percentage hold. If we assume the house edge is 2% and they play on average 15 hands, then the average hold will be around 25%, regardless of how much money they bring to the table. (The numbers here are wrong, but directionally correct).

Remember, as Turble said, hold is just an accounting term. If you came to the table with $100, and after each hand you cashed out and then cashed back in for $100 before playing the next hand, the hold would be 2%. You haven't changed the odds, you've just messed with their accounting.

Quote:
No, the house advantage would only be relevant in games like roulette where the house advantage is the same regardless of what "strategy" the player uses. In blackjack the house advantage assumes using basic strategy, which isn't even close to what the majority of players employ in real life.
Ahhh....so we should look at the average house advantage, which is the house advantage over the average player. That would cover both very good players and very bad players, both people who employ basic strategy and those who don't employ any strategy. I wonder if the UNLV cite I linked to has the house edge for the average player? Spoiler: It's 2%.

P.S. not knowing the difference between lose and loose is ignorant. What's the theme of this messageboard?

Last edited by Evil Economist; 04-09-2009 at 09:44 PM..
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  #38  
Old 04-10-2009, 12:38 AM
Sam Stone Sam Stone is offline
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Turble is exactly correct in everything he has said.

Let me try to help explain:

Quote:
Originally Posted by Fantome View Post
No, it's not. The question was, "What is each hand worth, on average, win or loose, to the House?"
On average, the 'average worth' of a hand to the house is the house's expectation. If a player plays blackjack perfectly - not card counting, but just playing the cards in an optimal way using basic strategy - the house's expectation ranges from about .25% to about .75% of each hand's bet. Let's use .5% as an average. So if the average bet size is $10, then the casino will stand to earn 5 cents per hand. If a full table has seven players and the dealer deals 100 hands per hour, the table will earn about $35/hr.

Now, not everyone plays perfectly. For example, many people stand on 15 when the dealer has a 7, which gives up a lot of expectation to the house. Some people use their 'intuition' to modify their strategy, which is always to their detriment. So the house's expectation againt the general public is somewhat higher than it is against a player who plays perfectly. The generally accepted number in the gambling literature is about 2% as a 'real world' expectation for the house. Given that, the house's expectation for the example above would jump from $35/hr to $140/hr.

Now... the HOLD is the ratio of money taken in to money paid out. This has nothing to do with expectation, and has more to do with the pyschology of the gambler, the addictiveness of the game, how pleasant the dealer is, whatever. It's something casino management cares about, but is completely irrelevant to the gambler in determining how much money per hand the casino gets.

The hold is higher than the expectation because players play through their money many times. For example, let's say you sit down at the table with $1000, and you play 100 hands at $10 per hand, and you happen to do exactly as well as the odds would suggest, so the casino makes exactly its expectation from you. The casino gets .5% of your money, and you're left with $995. But, being the gambler you are, you decide to keep playing. 100 hands later, and the casino has taken another .5%, and now you've got $990.25.

If you sit there and cycle your money through by playing 500 hands, then you get tired of playing and leave, you'd walk away with $975.25, and the hold for the house turns out to be about 2.5%. But if you're totally addicted and you sit there without bathing or sleeping until you're busted, the casino's hold is 100%.

Got it?
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  #39  
Old 04-10-2009, 06:53 AM
jakesteele jakesteele is offline
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Quote:
Originally Posted by Turble View Post
By George, I think I've got it … the explanation, that is.

The original question was “What is each hand worth, on average, win or loose, to the House?”

I'll rephrase that in more professional language. What is the Expected Value of a hand of blackjack?

EV = House Advantage x $Amount of the Bet

Example: A game in which the House Advantage, for whatever reason, is 2% (given different rules or different players that number can vary.) A player wagers $10.

EV = 0.2 x $10
EV = 20 cents … in other words, that bet on that game is worth, on average, win or lose, 20 cents to the house … and that will hold true for any given House Advantage and any given $ amount bet.

Clear? Nothing else needed. That is the answer to that question.

PS: Good job, Evil. They're all yours for now; I gotta go.
This is exactly what I was looking for, thanks.
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  #40  
Old 04-10-2009, 10:02 AM
Turble Turble is offline
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You're welcome.

Note that I slipped a decimal, however. It should read:

EV = 0.02 x $10
EV = 20 cents
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  #41  
Old 04-10-2009, 01:27 PM
YamatoTwinkie YamatoTwinkie is offline
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Quote:
Originally Posted by Sam Stone View Post

If you sit there and cycle your money through by playing 500 hands, then you get tired of playing and leave, you'd walk away with $975.25, and the hold for the house turns out to be about 2.5%. But if you're totally addicted and you sit there without bathing or sleeping until you're busted, the casino's hold is 100%.

Got it?
I get it now. What was throwing me for a loop is figuring out the difference between the hold of 1 person playing 1000 hands (house hold of 5% using your math) and 1000 people playing 1 hand (house hold of 0.5%)

...Then I realized that at $10 a bet, the buy-in for the 1000 people is $10,000, as opposed to the single guy that only bought $1000 of chips before starting
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