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#1




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? 
#2




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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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. Really? In that case, the casino would take in $1,848,000 per table. 
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#5




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.
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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:
Quadruple the house edge and you quadruple the expected value. Now your table is "expecting" $1.44 million a year. Quote:
Last edited by Cyberhwk; 04092009 at 01:37 AM. 
#6




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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. 
#7




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 noncounting 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 
#8




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. 
#9




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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#12




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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. 
#13




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 buyin 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; 04092009 at 01:02 PM. Reason: Edited to reply to jakesteele 
#14




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Average bet: $10 Casino hold: 22% The average casino worth for a hand played is $10 x .22 = $2.20 


#15




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

#16




Yes, it does.
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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:
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#17




I agree. But I think Turble is figuring in longterm expections, which for a single trial, with the house losing 6 $10 bets, doesn't mean anything.
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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; 04092009 at 02:14 PM. 
#18




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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#20




“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. 
#21




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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:
How can you then say the average worth of each hand to the house is only 2%? Quote:
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#22




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Everything. I can't tell if you are a troll or simply dense. /sigh Uncle. 
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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*
Last edited by pulykamell; 04092009 at 06:10 PM. 
#27




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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 buyin, 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




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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; 04092009 at 07:13 PM. 


#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




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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:
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Last edited by Evil Economist; 04092009 at 07:51 PM. 
#32




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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:
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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:
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#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. Last edited by Turble; 04092009 at 08:10 PM. Reason: Evil Economist has it. 
#34




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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




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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




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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 playersee 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:
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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:
P.S. not knowing the difference between lose and loose is ignorant. What's the theme of this messageboard? Last edited by Evil Economist; 04092009 at 09:44 PM. 
#38




Turble is exactly correct in everything he has said.
Let me try to help explain: Quote:
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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#40




You're welcome.
Note that I slipped a decimal, however. It should read: EV = 0.02 x $10 EV = 20 cents 
#41




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...Then I realized that at $10 a bet, the buyin 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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