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The "drift towards balance"

Discussion in 'Casino Gaming' started by Ruark, Apr 15, 2013.

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  1. Ruark

    Ruark Low-Roller

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    We all know of the concept of independent events. Take dice rolls, for example, with the numbers 1 through 6. A roll doesn't mysteriously "influence" the next roll, obviously. That's why if you roll a hundred times without getting a 4, your chances of rolling a 4 on the 101st roll are still 1 in 6.

    But is it? Yes, they are independent events, but if you made, say, 10 million rolls, you would NOT roll 10 million times without a 4. You would get each number occurring about 1,666,666 times. You WOULD. This is what I think is called the "drift towards balance," and it is undeniable.

    Does this defy the law of independent events? Is that probability of that 101st roll being a 4 REALLY 1 in 6? You would think that the longer you went without rolling a 4, the more likely the next roll would be a 4, because of the principle of drift towards balance.

    I was thinking of roulette and that system we were recently discussing. Say the bet is on any number 1 through 7. The odds of getting one of those numbers is about 1 in 5 in a single-zero wheel. The probability of making 20 spins without hitting one of them is about 1 in 60, I believe.

    So if you look at the history board and see that none of the numbers 1 through 7 have been hit in the past 30 spins, are you more likely to bet on them? Most people, probably including me, would hold up our forefingers and say, "no, they're independent events, silly!" OK, but what about the principle of drift towards balance? Are we denying that?
     
  2. Auggie

    Auggie Dovahkiin

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    Yes, the more times you roll the die the more the numbers will "drift towards balance" but that is a factor of the numbers themselves and not the die.

    As an example:
    If you roll a die 100 times the expectation is that each number will come up 16.6 times, or 16.6%
    If in those 100 rolls the number 4 comes up only 11 times thats only 5 below what you would expect but the number 4's hit frequency is 11%

    The difference between 11% and 16.6% is pretty big...

    Now if you keep on rolling to a total of 1000 rolls and lets say that for the next 900 rolls the number 4 comes up 150 times which is exactly how many times you expect in 900 rolls.

    So now for 1000 rolls your expectation is each number coming up 166.6 times and the number 4 is still five hits short of its expectation (the five times it was short in the first 100 rolls).

    So your expectation is that each number comes up 16.6% of the time but for the number 4 its actual hit rate is 16.1%

    And thats the "catch" here: the number 4 did not come up any more than expected for the next 900 rolls, it hit exactly as many times as expected, however the actual hit rate went from 11% to 16.1% --> the hit rate went UP without any positive or negative influence.

    And thats because the numbers will "drift towards balance" but the actual results and outcomes don't have to.



    And one other thing is: there is a huge difference between 100 spins of a roulette wheel and 1,000,000 spins.
     
  3. Kickin

    Kickin Flea

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    Yes

    If it went really really really long I'd think there was something wrong with the die which would be cool. I'm no craps expert but there must be a way to make some chedda' on that.

    I would but only because I'm a degenerate gambler and look for any excuse to place a bet, logical or not.

    You know if you had a monkey randomly typing letters for an infinite amount of time he'd eventually type out an exact copy of a Shakespeare play? Pretty crazy huh?
     
  4. Driven2ThEdge

    Driven2ThEdge Newbie

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    Yes...

    Come on now, it's very simple. The dice does not have any memory. It really is that simple.



    Think about it this way. Let's say we're flipping a fair coin. The first 10 flips happen to be heads. Right now it's 100% H and 0% T. The next flip is still 50/50, and so will every flip after that. After enough flips it will roughly be 50/50 again, but not because the odds were altered, but because when we increase the denominator in #of heads/# of flips is gets closer and closer to 50%.

    Take a look at this gif please. It should make everything very clear:
    http://upload.wikimedia.org/wikipedia/commons/4/49/Lawoflargenumbersanimation2.gif
    :beer:
     
  5. WrongWayWade

    WrongWayWade VIP Whale

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    YES IT IS!!!

    Not really, with 10 million rolls you'd see the percentage 4s very nearly 1/6th of 10 million, but being exactly or almost exactly 1,666,666 would be rare indeed.

    The problem with such a concept is that you don't know if it is going to happen on the next roll or next 10 rolls or next 100 rolls or never. If you've had too few 4s so far, you can just as easily have a lack of 4s in the immediate future.

    This was best explained to me this way: The numbers tend to approach the expected value because of INNUNDATION, not COMPENSATION. The odds of getting the 4 stay at exactly 1/6 on every roll regardless of the past, and that fact alone (there isn't any 'trying to make up for the lack of 4s'), makes the totals come out near the average.


    Yes, yes, 1000 times yes.

    No, 'drift toward balance' is NOT a principle, as it implies knowledge of the past results affects the future.

    Look at this example: You roll 20 times with zero 4s. But in the next 200 rolls you get the 'right' number of 4s = 33. So now your total percentage of 4s is 15%, getting rather close to the 16.7% you expect. There wasn't any compensation necessary (rolling more 4s than normal to 'make up for' the lack of 4s in the first 20), but you still approach, rather quickly, the expected percentage.
     
  6. vsop

    vsop Low-Roller

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    There's no denying the numbers...the problem is, how many rolls will it take before the stats start to "balance" out? Who, besides the house, has the kind of $$$ to find out?

    In games of chance such as craps and roullette, the human factor influences the outcome, not a computer/mathematical calculations...a player or dealer directly influences the outcome....the outcome is still random, but it is still influenced....
    in the end, it's still gambling...
     
  7. shifter

    shifter Degenerate Gambler

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    because of the human element, I think if you're going to pick one direction to go with, you're better off betting on numbers that are showing up more frequently rather than less. as long as the dealer has his hand on the ball each time, there's a possibility that he's influencing, however small, the result. for example I've talked to dealers at the Bacc table that just always deal player shoes. if you like banker, you don't play with them. they deal thousands of shoes a year, but more often than not player wins more than banker and often by a significant number. how is that when the cards don't have memory? the human element.
     
  8. bringyogreenhat

    bringyogreenhat Tourist

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    It's just numbers. A drift towards balance is your point of view.
     
  9. Kickin

    Kickin Flea

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    There's a possible human element in roulette that could bias the results. But not in baccarat. How? The dealer is just a monkey dealing out the next card based on the rules. Those dealers peddling that nonsense are just suffering from selective bias.
     
  10. shifter

    shifter Degenerate Gambler

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    don't really know how it works, but there is a small human element in Bacc since the dealers do shuffle and cut the cards. and I've experienced it first hand with some of these dealers that I've played with for years and see the same sort of shoes every time I play with them.
     
  11. RiddickBull

    RiddickBull VIP Whale

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    I agree with Shifter. I rarely play craps, but when I play, my friend always bet on the Field when I shoot. For some reason, I always get those numbers, even though the dice have no memory. He says I roll "ugly" numbers. It's one of those things that cannot be explained.

    From a mathematical point of view, you would say everybody has the same chance as rolling the Field, but for some reason it is not.
     
  12. Nevyn

    Nevyn VIP Whale

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    Were these serious questions, or just trolling the math people?

    Yes, the events are independent.

    The reason you can not get the 4 100 times and then still have 1 in 6 on the 101st roll is because the combined probability is different from the individual. You have already accepted the unlikeliest part as given. From there, the original odds apply. Or you can take the overall odds of it happening 101 straight times.

    The reason things appear to "drift towards balance" is because the number of iterations continues to increase. For example, if I flipped a coin 1000 times and got 750 heads, that would be a large variation. If I then flip another million and get exactly a half million of each, I have now flipped 500750 heads and 500250 tails. I have still flipped as many more heads than tails as I had before, but now that difference seems minor as the number of iterations has gone up substantially.
     
  13. Ruark

    Ruark Low-Roller

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    People, jeez, I'm fully aware that they are independent events. I just wasn't sure how to relate that to the drift towards balance as something "influencing" events. It's sort of fun to discuss something that some might blow off as irrelevant.
     
  14. mjamesp

    mjamesp High-Roller

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    Lack of sample size and selective memory could explain this
     
  15. BeeeJay

    BeeeJay President of The Red Lobster Hostess Satisfaction

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    <iframe width="420" height="315" src="http://www.youtube.com/embed/Qw9oX-kZ_9k" frameborder="0" allowfullscreen></iframe>
     
  16. shifter

    shifter Degenerate Gambler

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    maybe. but there are some things in the world just can't be explained. and luck is one of those.
     
  17. Kickin

    Kickin Flea

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    Ruark I get what you're saying and I like the sentiment of just discussing theoreticals even if they're not practical. What you're talking about is a common misconception amongst gamblers. Its probably most prevalent in roulette players. The idea of reversion to the mean happening within your small sample. The problem is you're almost never going to see a big enough sample size. If you actually did have a statistically significant sample size and there was a statistically significant deviation than I, personally, would rather bet there was some bias in the wheel instead of on things reverting to the mean. But for practical purposes it would be impossible for me to ever witness a large enough sample size in the first place and equally impossible for me to take advantage of it within a reasonable time frame and reasonable bankroll.
     
  18. BeeeJay

    BeeeJay President of The Red Lobster Hostess Satisfaction

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    Luck is what happens when preparation meets opportunity.

    Seneca
    Roman dramatist, philosopher, & politician (5 BC - 65 AD)
     
  19. shifter

    shifter Degenerate Gambler

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    I fully believe that in the realm of success in life. when people say some guy got "lucky" to make it big, they didn't see all the sweat behind the scenes for years that put him in the position to get "lucky". but random events like gambling are a different story. in my experience some people are just luckier than others for an unknown reason.
     
  20. BeeeJay

    BeeeJay President of The Red Lobster Hostess Satisfaction

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    It shouldn't be true theoretically, but it is so true in my experience as well. Perhaps it is because Fate favors us. :evillaugh
     
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