Blackjack - average value per hand

Factual Questions
21

I’m not following you. What is this 2% supposed to reflect?

Right. Why should I have described anything else? What did Ido wrong here in your eyes?

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?

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?

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%?

You said:

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.

22

/sigh
Everything.

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

/sigh
Uncle.

23

Moderator note

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

Colibri
General Questions Moderator

24

Understood. I had tried to delete it but missed the edit window. Sorry.

25

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.

26

nevermind

27

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.

28

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.

29

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.

30

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?

31

Yes, but not for the reasons you think; see below.

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:

The link also gives the house edge for Blackjack at

32

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):

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.

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:

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.”

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%.

That’s not what you said.

33

“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.

34

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.

The house edge would give him that number quite nicely. That’s 2%.

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.

The UNLV webisite I linked to defined it the way I do, which is differently than you do. Do you have a different cite?

No, what I said was correct.

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%.

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?

35

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.

36

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?

No, he doesn’t. It’s a common spelling mistake and that comment wasn’t really necessary.

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.

You believe the OP asked what the house edge is if everyone sticks to the basic strategy? That’s not what he asked.

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.

What? I said the answer to YamatoTwinkie’s question is “no” if we’re defining hold as you have.

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.

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.

37

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?

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 600,0006102%=$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 600,00010*2%=120,000.

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

Very good, except your answer was wrong.

The answer to YamatoTwinkie’s question is “yes,” if we define hold the way I have.

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.

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?

38

Turble is exactly correct in everything he has said.

Let me try to help explain:

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?

39

This is exactly what I was looking for, thanks.:smiley:

40

You’re welcome. :slight_smile:

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

EV = 0.02 x $10
EV = 20 cents