Blackjack - average value per hand

[jakesteele]

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?

[Rigamarole]

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.

[Fantome]

@jakesteele

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?

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?

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.

@jakesteele

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.

[Fantome]

@jakesteele

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.

[Cyberhwk]

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.

@jakesteele

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.”

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:
[ul]
[li]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.[/li][li]Add on another 2-3% if there is considerable play on a bonus bet.[/li][/ul]

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

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.

[Cyberhwk]

@Fantome

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.

[Quercus]

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

[Turble]

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.

[Pleonast]

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.

[Fantome]

@Cyberhwk

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.

@Quercus

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.

[Fantome]

@Turble

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%.

[jakesteele]

@Fantome

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.

[Turble]

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.

[Fantome]

@jakesteele

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

[Turble]

Fantome, you still aren’t getting what Hold means in casino lingo.

[Fantome]

@Turble

RE: When the house loses six $10 bets it does not lose $60.

Yes, it does.

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?

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?

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?

Fantome, you still aren’t getting what Hold means in casino lingo.

What makes you say that?

[pulykamell]

@Fantome

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.

Where are you getting this 2% figure?

I assume that’s the house edge on blackjack, given perfect, or near-perfect play.

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?

[Turble]

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.

[Fantome]

@pulykamell

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.

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.

@Turble

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.

[Turble]

“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.