The following excerpt is from the March, 2007 issue of Anthony Curtis' Las Vegas Advisor:Nevada gamblers risked $11.2 billion at the blackjack tables in 2006, a 6.1% increase over the 2005 handle. Of that, the casinos won $1.38 billion, a big jump of 11.1% over 2005. The 2006 casino hold on blackjack amounted to 12.3%. It was the biggest handle and hold of any table game.The Good News: Blackjack is thriving. The Bad News: My guess is the big profit move is due to the proliferation of "bad rules". Also, with a "hold" of 12.3% tells me a lot, make that a whole lot, of players know nothing about the game and basic strategy is staying unread in the book stores. It is indeed a PLOPPY PARADE.
Let them keep flocking to Vegas, let it continue. Heck, there is so much else to do and see there it makes up for it all.....
That's crazy. Not only is basic strategy being ignored, whatever strategy people are using is terrible! From Wizard of Odds, if you play never to bust (stand on 12 and up) you give the house around a 3.9% advantage in S17 games. If you mimic the dealer (no doubling or splitting, S17), you give the house an edge of 5.5%. Just what the heck would you have to do to give the house 12.3% edge?? And that's just the average! For every person who plays basic strategy, that's an average of someone who's giving the house 24%! You may as well surrender every hand and wait for blackjacks! (More likely for every person playing basic, it's about 50 people playing at 13% house advantage, but still...)
WumpieJr, You are confusing "hold" with "house edge". They are not the same. The "hold" is how much the casino keeps of your buy-in. For example: Let's say you buy-in for $100. You play 100 hands @ $10 and you lost $5. The house edge is 0.5% ($5 / ($10 * 100). The HOLD is $5 or 5% ($5 / $100).
House edge the casinos can actually make a positive hold off of an even money game - as they have a huge advantage - they have the bigger bankroll - meaning they can survive the losing streaks better than the players do - even in an even money game - the player and the house will both hit long losing streaks eventually - bad periods - the house survives these to eventually win back their money - the player goes bankrupt and leaves all of his/hers behind - also - credit bad money mangement - if players win - they start betting larger amounts - until they lose it all back -
Aah, I was wondering what that was about. I'm still a little confused. Where does the 100 come from in calculating the HOLD? If the calculation is $5/100 hands, what you have isn't a percentage, it's a number of dollars per hand. Is that how it should be labeled? Also, RKuczek, I was having an argument with my friend once about 100+% slots. I said that casinos can afford to have slots that pay out slightly above 100% because the players leave when they're bankrupt, the same logic you used here. He countered with the following scenario: Take a single slot machine with a 100.0001% payout rate. Over time, players will visit that machine and it will continually pay out just a little more than it takes. Some of those players will go bankrupt and leave with their losses. Some will leave with wins. However, after 10 years of play, the machine can't tell the difference between the players. It may as well have been one player playing continuously with an enormous bankroll for all the machine knows. It has dutifully payed out that .0001%. The fact that some players went bankrupt doesn't change the fact that the machine loses money. That just changes what butt is in the chair. Say the machine played 2,000,000 hands. No matter how much money the players had when they played, whether some of them went broke, whatever, the machine still payed out on 1,000,001 and took on 999,999 (assuming 1:1 payout, you get the idea). I have yet to come up with a counter-argument. Perhaps the seasoned members of this site can help ^_^
The "100" is the "$100" that you bought in for. So to restate: You buy in for $100. Your lose $5 The hold is 5% NOTE: I will edit my original post to reflect the dollar numbers.
Oh, I see, so "risked" means "brought to the table." So we'd need an average number of hands played per sitting to get a real EV. Thanks for the explanation.
Don't feel bad Wumpie. I've seen people in the casino business for years that still don't understand the difference between house edge and hold. As for your slightly over 100% slot machine, your friend is absolutely right. The machine will lose money, regardless how many players it bankrupts. RKuczek's even money game example will also produce daily holds that vary from negative to positive, centered on $0. For some reason, I am reminded of an old Saturday Night Live skit where a store was selling items at a loss. They planned to make their profit with "Volume, Volume, Volume."
House Edge Toolman, I'm sure you know this about "house edge" but your anology is maybe confusing to new (or less educated) players. House edge does not have anything to do with what you loose (or win) but has to do with the pre-defined set of rules of your particular game and the strategy a player uses. So in Wumpie's post, the initial "house edge" of one particular game with a set of rules has a constant house edge. Wumpie then goes on to quote various (bad) versions of strategy plays. The initial "house edge" is calculated by the rules of the particular game with the assumption that the player is using sound basic strategy for that particular set of rules. The actual wins or loss of the players combine to make up the "actual hold" of the casino on that game. The "estimated hold" would be based on the assumption of the skill of the players playing those games. It's all about the math involved in the game. Dan
House Edge I take this to mean you could calculate a mean house edge over all players by dividing total hold by total amount wagered (handle.) 12%? Wow! Some combination of the following factors must be at work here: Tokes are included in the hold. Horrible players Horrible rules Inaccurate methodology for compiling the stats Crooked games (unlikely to be significant) Blackjack machines that pay 1:1 on BJ's included in stats
Nothing so sinister The primary factor that the "hold" is higher than the "edge" is that people continue to play. i.e. If on the average, the "edge" is 0.5% and one buys in for 100$ and plays 10$ 240 times, the average hold will be 12.0%. Chips
It's not just the rules or even just bad play that make for a high "hold". As I pointed out in my example in post #4: The actual house edge can be 0.5% while the hold can be 5% for the same play. To calculate "hold", the divisor is the buy-in amount. To calculate "edge", the divisor is the total amount wagered (or coin-in in slot player terminology). Just to clarify: When you say "I take this to mean you could calculate a mean house edge over all players by dividing total hold by total amount wagered (handle.)" This would be the actual house edge for all play. This will differ from the theoretical house edge of 0.5% for a basic strategy player which remains constant as DanMayo pointed out in an earlier post. The problem is, to arrive at the actual edge the house enjoyed for the time period in question you need to know how much was actually wagered in addition to the hold. The hold percentage will virtually always be greater because divisor will virtually always be smaller. So "hold" cannot be compared to "edge". It's like comparing apples and oranges. Looking at it another way: The "hold" can be thought of as a simplified "gross profit". But of course, casinos always shy away from using the word "profit". They devised other words to take the place of "profit". For example, at the end of a day the casino counts it's cash. It then sets aside X amount to cover what's need to operate. The balance is sent to the bank. The amount sent to the bank is called "excess". I think that's a cute name for "gross profit". I would like to have the "excess" from just one Saturday at a major casino.
Ken I have to respectfully disagree with you - the casinos can make a profit off of even money games - there have been many mathematical studies of the "Gambler's Ruin" problem in probability - which anyone can track down on the internet - including studies of games involving n-players - which would apply to casinos' profitability - when you include the psychological characteristics of real world gamblers - and their irrational behavior (talking about 'recreational' gamblers of course - not anyone connected with/posting on bjt.com:joker: ) - a well run casino will be profitable off of even money games - with even a very slight edge for the house - actually any edge at all favoring the house - no matter how minute - casino management must be extremely incompetent not to make a substantial profit - because of the impact of even the very smallest house edge on "Gambler's Ruin" - If you want to explore something potentially interesting for gamblers - there have been a number of studies done on methods for detecting 'change points' in a brownian motion process- that is - how to tell when the series of wagers has turned positive/negative for you -
Gamblers Ruin When thinking of the casino's viewpoint in terms of gamblers ruin you have to analyze the players together as a whole. The names and faces may change but the entity, "player" remains the same. Individual players may be ruined by being out-bankrolled by the casino. But the players as a whole just keep coming and coming. The casino does not have the players, taken as a whole, out-bankrolled. This fact is why casinos have to impose table limits. They have a limited bankroll. Bill Gates can't walk into a small town Indian casino in Wisconsin and start betting a million a hand. He has the casino out-bankrolled and they would soon be ruined, in spite of the house edge in their game.
The wikipedia article on Gambler's Ruin doesn't defend the proposition that the casinos will benefit from an even money game, could you link to an article that explains that? Also, could you link to a page that describes how studies of brownian motion could lead to prediction of events? What you are basically saying there is that you could, simply by observing a player's BR change, predict when he/she should bet big. But that, of course, depends only on the cards in the deck. So this means you are saying that you could somehow observe the player's bankroll and predict something about the unseen cards in the deck. That seems unlikely ^_^.
casino's win Wumpie a possible counter-argument for your friend might be that the slot pays 100.001 only to perfect play. The slot is perfect the players are not. The only machines that have these kind of returns are video poker. Which require perfect play to get the complete edge. Even if a slot was set up to pay 100.001 the players still can make mistakes like forgetting to put in max. coins or walk away with a winner on the slot. ect. Murphy's law is on the side of the casinos. tgun
Some Citations for Wumpie Wikipedia is a very weak and often inaccurate source much of the time - some of their stuff is very good - some is garbage - their mathematical articles are usually simplistic and far away from anything 'cutting edge' - anyone interested in the mathematics of gambler's ruin, stopping points, change dection, etc. - might start with these - most are not available on the internet - unless you have subscriptions to the journals - but you can access the journals at university libraries - these areas of probability are being applied for investments in equity and derivative markets today by hedge funds and very sophisticated investors - remember that Thorpe went on to make his fortune (estimated by one source at over $350,000,000) by operating a hedge fund - as far as casino profits go - you can't just look at basic gambler's ruin formulas - nor assume that you can treat a large group of players as the equivalent of one continuous player - a group of players with limited bankrolls is not the mathematical equivalent of one player with an unlimited bankroll - it is a series of n-player games with each individual player having a very small bankroll compared to the casino's - you also need to consider player behaviors - which can be self-destructive - casinos get an advantage from players' self-destructive decision making in many cases - such as has been commented on this site - that 99% of bj players don't know/use basic strategy - thereby granting the house a larger edge - if bj was an even money game for the player - 99% would still play at a disadvantage to the house Change-point detection of two-sided alternatives in the Brownian motion model and its connection to the gambler's ruin problem with relative wealth perception Olympia Hadjiliadis, COLUMBIA UNIVERSITY http://mathworld.wolfram.com/GamblersRuin.html (some brief general comments - they state their opnion that gambler's ruin is the primary source of casino profits - disagreeing with Wikipedia) William Feller, An Introduction to Probability Theory and Its Applications, Vol. I, 3rd ed., John Wiley & Sons, New York, 1968. (some basic stuff that covers gambler's ruin in this text) http://www.aci.net/kalliste/Chaos4.htm Extensions of Gambler's ruin with even odds: multinomial and other models SOBEL Milton (1) ; FRANKOWSKI Krzysztof (2) The gambler's ruin problem with n players and asymmetric play Authors: Rocha A.L.; Stern F. Source: Statistics and Probability Letters, Volume 44, Number 1, August 1999, pp. 87-95(9) Publisher: Elsevier A new formula on a particular type of «Gambler's ruin» problem withN players Journal Decisions in Economics and Finance Publisher Springer Milan ISSN 1593-8883 (Print) 1129-6569 (Online) Subject Business and Economics Issue Volume 4, Number 1 / March, 1981 DOI 10.1007/BF02091806 Pages 39-45 Stochastic Optimization and the Gambler's Ruin Problem I. O. Bohachevsky, M. E. Johnson, M. L. Stein Journal of Computational and Graphical Statistics, Vol. 1, No. 4 (Dec., 1992), pp. 367-384 doi:10.2307/1390789 Drawdowns Preceding Rallies in the Brownian Motion Model Olympia Hadjiliadis, Princeton University, Department of Electrical Engineering. Jan Vecer, Columbia University, Department of Statistics.
Here's the example from one of the links: An Example You have $10 and your friend has $100. You flip a fair coin. If heads comes up, he pays you $1. If tails comes up, you pay him $1. The game ends when either player runs out of money. What is the probability your friend will end up with all of your money? From the second equation above, we have p = q = .5, W = $10, and R = $100. Thus the probability of your losing everything is: 1 - (10/(10 + 100)) =.909. You will lose all of your money with 91 percent probability in this supposedly "fair" game. ----------------------------- RKuczek, extending this particular example, you are asserting that the friend with $100 will make money in the long run, if he repeatedly challenges friends with only $10 each to play this game. Is that a correct characterization of your position? I don't see how that can be the case. Time for another simulation?
Coin Flip A fair coin is a 50/50 proposition, no matter who you're betting against and no matter the history of the previous bets against any given opponent. The fact that the $100 dollar player ruins $10 players most of the time doesn't change this basic 50/50 fact. Lets use an extreme example to illustrate this principle. Lets change the big player's bankroll from $100 to $100,000,000,000. Lets say we have the entire population of China lined up each with $10 waiting to play this game. As soon as one Chinese player bombs out the next in line takes his turn. What will be the mathematical expectation of the big player's bankroll after one hundred billion coin flips? It should be fairly close to $100B. The big player's wins and losses will have been roughly equal, the expected outcomes being a normal distribution. Lets say on the next table we have two $100,000,000,000 players going head to head. What is their expectation? Is the outcome of coin flips different because a long line of opponents went up against the big player rather than an equally big player, playing the same game?
