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How many trials needed to verify existence of and size of the house edge ??

Discussion in 'Casino Gaming' started by bklynkid1, Aug 29, 2015.

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  1. bklynkid1

    bklynkid1 Newbie

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    Hello folks,. I have often wondered when playing live casino games such as blackjack, what amount of hands played or trials are necessary to verify the existence and size of the house edge. Let's say you sit down at Blackjack and you simply flat bet every hand using a fixed hand play strategy along with the table rules that yields what should be a House edge of + 1/2 %. What is the LEAST number of hands you would need to have played in order for that edge to show itself "moneywise" with near certainty. Or said in a different way, "If I keep playing this game by the time I have played out " Z " number of hands, any edge and it's size will show up in my bankroll result. I know there are some fairly sharp cats and kittettes around this place and I would certainly appreciate the help. Thanks, Bklynkid 1
     
  2. alexanbo

    alexanbo High-Roller

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    0, the math doesn't change no matter how many hands you play.

    If the question is how many hands do you have to play to guarantee you'll lose exactly the house edge as predicted by the math, then there is no number of hands that will guarantee that because of variance.

    To illustrate that there's always some non-zero chance that however many hands you play you'll win every hand.
     
  3. zignerlv

    zignerlv Low-Roller

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    I like Alex's reply, but here is another way of looking at this. What is sounds like (unless I am reading too much into your question) is that you want to verify that the published odds of the game you are playing is correct by verifying the house advantage percentage through your play. If that is your question, then I would take another route and first ask why question the math? And then, if you really wanted to question the math, the best way to verify it would be to run some simulator software through a million or so hands, using your preferred strategy. You would then approach the expected return, very closely. If you instead wanted to try this through your own play in a casino, you would need hundreds of hours of play, and just as importantly, highly accurate tracking of your play, to get that data. That would be a burden.
     
  4. PayTriple

    PayTriple The Cucumber King

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    This is why I gamble: even though the house has an advantage, because of variance, there exists a mathematical possibility that I can win on any given bet, session, trip, year, decade.
    And if I'm really "lucky", perhaps win over my lifetime! (But I wouldn't bet on it).
     
  5. Chuck2009x

    Chuck2009x VIP Whale

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    Alexanbo is correct, the real answer is zero, the math is immutable.

    However, an alternative answer is: 1 winning hand. The house edge is the difference between the probability of an outcome, and the amount you actually get paid when it occurs.
     
  6. Snidely

    Snidely VIP Whale

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    As the number of trials approaches infinity, the observed house advantage approaches the theoretical house advantage.

    Here's a simple example: Take a fair coin, Assume it's a perfect 50/50 heads or tails. The house always takes tails. The player, you, always takes heads. After a million trials with a flat bet are you going to be exactly even with the house? No, you'll be close to even but not exactly even. If you graph the line of money won/lost it will have variance and ups and downs but eventually it will settle down and approach zero.
     
  7. PayTriple

    PayTriple The Cucumber King

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    Actually, if you do a million trials, the Percentage will be close to 50/50, but the Absolute difference from 500,000 will likely be substantial. In other words you could be up 1,000 or down 1,000, for example, but it is highly unlikely that you will be up or down exactly 0.
    Note that even the 1,000 either way is small compared to 500,000, so the percentage is close to the theoretical 50%.
     
  8. Nevyn

    Nevyn VIP Whale

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    Yeah, there is no real answer here. As alex said you don't need trials, as the edge can be calculated.

    And as others said, there isn't a set hand at which the results are guaranteed to exactly match, instead they approach the theoretical edge over time. And doing it as a practical experiment would also depend on unlimited bankroll and perfect basic strategy.

    The closest thing to what you are asking is the standard deviation analysis at Wizard of Odds.http://wizardofodds.com/games/blackjack/appendix/4/[/URL , specifically the probability of loss table.

    Assuming a 0.4% house edge, according to that table sometime between 10000 and 20000 hands, you would reach a point where there was a 0.01% or less chance that you were still up (ie: a point at which you are virtually guaranteed to be losing). If you make the standard of 'proof' a 99% chance of being down instead, you are talking around 5000 hands.

    So that many hands would 'prove' the existence of the house edge, but would not be sufficient to reliably calculate the extent of it.
     
  9. shifter

    shifter Degenerate Gambler

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    The answer is infinity.

    If the house played the house infinity hands, the actual HA would be exactly the theoretical HA.

    Any fewer and variance will be in play.
     
  10. nostresshere

    nostresshere Mr. Anti Debit Card

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    As said, there is no way to do this.

    Statistically, it gets closer with millions of hands. But, it could also swing one way or the other at any time. Each hand is independent of the next (other than cards in that particular deck/shoe). Once they start a new deck/shoe, lady luck knows NOTHING about the last deck/shoe. NOTHING.

    And, you ASSUME you play perfect. Nobody does that. Hitting, standing, doubling, etc.

    No offense to the OP, but this reminds me of the comments from time to time about slots. Someone will come here and say " I think I will put $1,000 in a machine with 90% payback and worse case - see a $100 loss" I think some of those folks actually believe that.
     
    Last edited: Aug 30, 2015
  11. Auggie

    Auggie Dovahkiin

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    To verify the existence, and the size, of the house edge you don't need any hands, just math (statistics).

    The house edge can be determined by taking the probability of all events happening in a game and comparing it to how much is returned to the player when the event occurs.

    This is most easily calculated in roulette: if you are sitting at a 00 wheel (a wheel with both 0 and 00 spots) and put a chip down on the board there are 38 spots on the board, but other than the "basket bet" the game pays you as if there are only 36 spots on the board... those two extra spots you don't get paid for are the house edge.

    So if you put a chip on number 17 you will get back 36 chips, but the odds of hitting number 17 are 1 in 38 (because of the 0 and 00 spots).
    Therefore the payback of game is 36/38 = .947
    The house edge is just an inverse (subtract from 1.00) of the payback: 1 - 0.947 = 0.053 = 5.3%

    All the outside bets are the same: if you bet on BLACK there are 18 black spots, 18 red spots and 2 green spots. You get paid back 2 to 1 on your bet so you multiply the 18 (number of winning spots) by 2 (how much you get paid back) and divide by the the total number of spots, which is 36/38 again, which = .947
    Likewise if you bet on 12 there are 12 winning spots, pays 3 to 1, and 24 losing numbers plus 2 green numbers... (12*3)/38 = .947


    This is actually a good example of why going for number of hands doesn't really work: if you are betting $5 a hand at blackjack on a table with a half percent house edge that house edge per hand works out to two and a half cents per hand.

    The casino doesn't have half cent chips and there is no betting combination that you could make that would only win or lose 2.5 cents, so you would have to turn that in to a betting unit ($5 in this example) which means you would need $5/.025 = 200 hands before you could be down just by the house edge.


    That 200 hands mentioned above is the minimum number of hands... technically.

    The problem is: it doesn't work that way. The house edge exists on every hand, even ones you win (which you winning any money on any hand is contrary to the house edge), and it doesn't manifest itself like "if you play 200 hands you will only be down 1 betting unit because there is only a 0.5% house edge"

    Instead it all goes back to the beginning: the house edge is the probability of an event happening versus its payout and while it can be calculated on a per hand per player basis it only really manifests itself when the casino looks at it from a big picture point of view, like all the hands played in the past week, month or year.
     
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