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Lucky and unlucky streaks can and do last months to years for people who play thousands of hands per day. This cannot possibly, possibly be true. The expecte

by Eliezer 16y ago

Lucky and unlucky streaks can and do last months to years for people who play thousands of hands per day. This cannot possibly, possibly be true. The expected deviation goes as the square root of the sample size, which means that the percentage deviation goes as the inverse square root of the sample size, which means that if you play thousands of hands a day for a year, your deviation ought to be less than 1%. Anything that persists over 100,000 samples is not luck.

erikb 16y ago
You mean it is quite unlikely that somebody has luck for as long as 100k hands or more. But the funny thing about "unlikely" is, that it occurs if you let a big group of people do the same stuff (like playing poker online). It is actually very, very likely that there are some (few) people who are hitting the luck box for much longer then just 100k hands. 1% seems to be a small number in your mind, I guess. Take one million people and if the chance to hit the jackpot is 0.1% you still get around one thousand people, who are lucky enough. Maybe everthing changed, but in the early days of online poker, 6 or 7 years ago, we said that you need around 600k hands to have some(!) trust in your win rates (your Big Blinds per hundred hands, to be precise).
danenania 16y ago
The statistical math involved in determining standard deviation in poker is a lot more complex than you're giving it credit for. A hand itself is a very large set of potential outcomes, not just a win/lose scenario. 100,000 hands is nothing. Ask any long time pro who understands the game. I've personally known several who play a very consistent, disciplined style against a consistent level of opponents whose results would vary greatly across 100k hand sets, from being a huge winner to barely breaking even to losing even though they all were at least steady winners overall. When you get in the 500k+ realm, it starts to get more reliable, but even streaks of this size are possible at the statistical fringes.
- Eliezer 16y ago
  Still skeptical. What happens when you have pokerbots play against each other? Do they have similar variance across 100,000 hands?
  - danenania 16y ago
    Yes. Some of the first statistical analyses of poker I came across when I was learning were based on simulations using bots run by none other than Nate Silver (he used to be a poker pro). His conclusions were in line with what I've been saying, and these simulations were using full and 6-handed tables if I remember correctly. Heads-up has even more variance.
    - Eliezer 16y ago
      Er, sorry but I don't suppose you've got a link? Let's say you came out even after 100,000 hands. If I randomly divided those hands into two sets of 50,000 each, would you expect one of those sets to be up by 10% and one of those sets to be down by 10%?
      - danenania 16y ago
        Wish I did but it's buried deep in the archives of the twoplustwo.com forums. You'd probably stand a better chance of finding it by contacting Nate and seeing if he has a copy of the writeup lying around still than using their godawful search interface. Not sure I understand your other question. There are no percentages in particular that I would 'expect', but if you ran the sim enough times then yes they'd revert to some mean. I've never done such analysis so I don't know what the results would look like.
        Eliezer 16y ago
        K - thanks for answering!
        danenania 16y ago
        Not sure if you're still following this thread, but another major factor is that only a very small percentage of hands actually have much monetary significance. At a full table in limit Hold 'Em, a strong player will fold ~80-85% of his hands preflop, and of those that go to the flop, only ~40% of those go to a showdown, and only a fairly small percentage of those are medium to large pots. Luck on these bigger pots has a huge impact on overall win rate, but in a set of 100,000 hands, you may only be involved in 2-3000 of them, and you may only expect to win something like 400 or 500 (very rough estimates). Maybe that helps explain why there's more variance than you might expect in a seemingly large sample.

by Eliezer 16y ago

erikb 16y ago

You mean it is quite unlikely that somebody has luck for as long as 100k hands or more. But the funny thing about "unlikely" is, that it occurs if you let a big group of people do the same stuff (like playing poker online). It is actually very, very likely that there are some (few) people who are hitting the luck box for much longer then just 100k hands. 1% seems to be a small number in your mind, I guess. Take one million people and if the chance to hit the jackpot is 0.1% you still get around one thousand people, who are lucky enough. Maybe everthing changed, but in the early days of online poker, 6 or 7 years ago, we said that you need around 600k hands to have some(!) trust in your win rates (your Big Blinds per hundred hands, to be precise).

danenania 16y ago

The statistical math involved in determining standard deviation in poker is a lot more complex than you're giving it credit for. A hand itself is a very large set of potential outcomes, not just a win/lose scenario. 100,000 hands is nothing. Ask any long time pro who understands the game. I've personally known several who play a very consistent, disciplined style against a consistent level of opponents whose results would vary greatly across 100k hand sets, from being a huge winner to barely breaking even to losing even though they all were at least steady winners overall. When you get in the 500k+ realm, it starts to get more reliable, but even streaks of this size are possible at the statistical fringes.

Eliezer 16y ago
Still skeptical. What happens when you have pokerbots play against each other? Do they have similar variance across 100,000 hands?
- danenania 16y ago
  Yes. Some of the first statistical analyses of poker I came across when I was learning were based on simulations using bots run by none other than Nate Silver (he used to be a poker pro). His conclusions were in line with what I've been saying, and these simulations were using full and 6-handed tables if I remember correctly. Heads-up has even more variance.
  - Eliezer 16y ago
    Er, sorry but I don't suppose you've got a link? Let's say you came out even after 100,000 hands. If I randomly divided those hands into two sets of 50,000 each, would you expect one of those sets to be up by 10% and one of those sets to be down by 10%?
    - danenania 16y ago
      Wish I did but it's buried deep in the archives of the twoplustwo.com forums. You'd probably stand a better chance of finding it by contacting Nate and seeing if he has a copy of the writeup lying around still than using their godawful search interface. Not sure I understand your other question. There are no percentages in particular that I would 'expect', but if you ran the sim enough times then yes they'd revert to some mean. I've never done such analysis so I don't know what the results would look like.
      - Eliezer 16y ago
        K - thanks for answering!
        danenania 16y ago
        Not sure if you're still following this thread, but another major factor is that only a very small percentage of hands actually have much monetary significance. At a full table in limit Hold 'Em, a strong player will fold ~80-85% of his hands preflop, and of those that go to the flop, only ~40% of those go to a showdown, and only a fairly small percentage of those are medium to large pots. Luck on these bigger pots has a huge impact on overall win rate, but in a set of 100,000 hands, you may only be involved in 2-3000 of them, and you may only expect to win something like 400 or 500 (very rough estimates). Maybe that helps explain why there's more variance than you might expect in a seemingly large sample.