Kelly criterion: from Phil Laak Q&A

[pete fabrizio]

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I made that mistake because my personal standard deviation is 85 big bets

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[img]/images/graemlins/confused.gif[/img] Wow.

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Yeah it is extremely high. That's based on less than 20k hands of 6-max, but it shouldn't matter b/c SD converges very quickly. Running around 30/28. I 3 and 4-bet a lot more than most.

[threads13]

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PokerTracker, over your intuition. Neither my suggestion of an 8 PTBB/100 (16 big blinds/100) win rate nor my suggestion of a 40 PTBB/100 (80 big blinds/100) standard deviation are extreme or unusual.

You've given no reason to call my figures unrealistic.

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I strongly believe that nobody or only few people in the world have true winrate of 8ptbb/100 (by true winrate I mean that its their EV in their games).
All stats threads suffer from same biase : mainly winners post stats and they mainly post about their hot runs. We didnt see many 500K+ hands screenshosts but many many people on these forums played 500k+ hands.
I think intuition/experience in the games is much better guidance here than some random stats people decided to post.

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I would speculate that this is an accurate statement.

Who doesn't like a little ego-inflation? [img]/images/graemlins/smile.gif[/img]

[bema03]

Does the Kelly Criterion suggest how big your bankroll should be? I thought it only suggested the fraction of your bankroll that you should risk based on several factors. I'm not trying to determine how many buy-ins I should have in my bankroll; I'm trying to determine how much of my bankroll I should risk. Under the Kelly Criterion, you're going to risk a different amount every time you sit down, unless you broke exactly even during the previous session.

For example, let's say my bankroll is $1800 and I want to play at a no-limit hold'em table (buy-in and blinds are irrelevant unless the final amount of money I decide to buy-in for isn't within the min/max buy-in range of the table). Let's further assume that the generic odds of me winning during this session, at a 10-handed table, are 1-to-1 (that is, half of the table wins, half of the table loses), and thus, b=1. Let's further assume that I think I can have a winning session 60% of the time (p=0.6, q=0.4). Then the fraction of my bankroll to risk, f, would be ((1*0.6)-0.4)/1, or 1/5. If I want to go Half Kelly, f would be 1/10. So I should bring $180 to the table, correct?

Then, let's assume I win $900 during that session so my bankroll increases to $2700. During my next session, if I assume the same numbers, I should bring $270 (2700 * 1/10) to the table, correct?

Thanks again.

[pete fabrizio]

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Does the Kelly Criterion suggest how big your bankroll should be? I thought it only suggested the fraction of your bankroll that you should risk based on several factors. I'm not trying to determine how many buy-ins I should have in my bankroll; I'm trying to determine how much of my bankroll I should risk. Under the Kelly Criterion, you're going to risk a different amount every time you sit down, unless you broke exactly even during the previous session.

For example, let's say my bankroll is $1800 and I want to play at a no-limit hold'em table (buy-in and blinds are irrelevant unless the final amount of money I decide to buy-in for isn't within the min/max buy-in range of the table). Let's further assume that the generic odds of me winning during this session, at a 10-handed table, are 1-to-1 (that is, half of the table wins, half of the table loses), and thus, b=1. Let's further assume that I think I can have a winning session 60% of the time (p=0.6, q=0.4). Then the fraction of my bankroll to risk, f, would be ((1*0.6)-0.4)/1, or 1/5. If I want to go Half Kelly, f would be 1/10. So I should bring $180 to the table, correct?

Then, let's assume I win $900 during that session so my bankroll increases to $2700. During my next session, if I assume the same numbers, I should bring $270 (2700 * 1/10) to the table, correct?

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No. Originally the Kelly Criteria was used to determine the fraction of bankroll to bet in Blackjack, but it can be adapted pretty easily to poker. For a comprehensive treatment, again I would recommend looking at Mathematics of Poker. But given winrates and standard deviations for two different games, the Kelly Criteria can tell you at what size bankroll you should be playing one instead of the other, in order to maximize bankroll growth. I believe I posted the formula earlier in this thread.

[curious123]

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Originally the Kelly Criteria was used to determine the fraction of bankroll to bet on teh ponies

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fyp </nit> [img]/images/graemlins/tongue.gif[/img]

[antistuff]

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Are you going to retract or apologize for saying that my figures were unrealistic? The only thing you have accomplished in this discussion is to object to something correct.

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I don't know why you are taking this so personally. I see no reason to apologize for saying something completely inoffensive, nor to retract a statement that I still believe is true.

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You behavior exemplified a type of willful stupidity I find repulsive, which is common on these forums, but which can be rejected here more easily than elsewhere due to the low tolerance for nonsense.

I posted that the common bankroll heuristics are inconsistent, and gave a simple mathematical tool for seeing this and assessing your own bankroll requirements. You found my message counterintuitive... which is part of why I knew it was worth saying. Fine. But instead of learning from it, you objected rudely and maintained your objection in the face of more and more empirical evidence that I am right. If you still insist I'm wrong, please be willing to wager a large amount of money on it.

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wow you're a jerk.

[uDevil]

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Are you going to retract or apologize for saying that my figures were unrealistic? The only thing you have accomplished in this discussion is to object to something correct.

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I don't know why you are taking this so personally. I see no reason to apologize for saying something completely inoffensive, nor to retract a statement that I still believe is true.

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You behavior exemplified a type of willful stupidity I find repulsive, which is common on these forums, but which can be rejected here more easily than elsewhere due to the low tolerance for nonsense.

I posted that the common bankroll heuristics are inconsistent, and gave a simple mathematical tool for seeing this and assessing your own bankroll requirements. You found my message counterintuitive... which is part of why I knew it was worth saying. Fine. But instead of learning from it, you objected rudely and maintained your objection in the face of more and more empirical evidence that I am right. If you still insist I'm wrong, please be willing to wager a large amount of money on it.

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wow you're a jerk.

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No, he's one of the most helpful posters on 2+2. He just takes math and logic very seriously.

[jfk]

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No, he's one of the most helpful posters on 2+2. He just takes math and logic very seriously.

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Plus, he takes an extraordinary amount of time to compose educational, well considered threads which have benefited countless readers.

pzhon is something of a legend at 2+2.

The sole purpose of this reply is to let him know that his efforts are deeply appreciated.

[Abbaddabba]

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After looking at the SD's for the 100+ players in my database with the most hands played, I do think that my 85 ptbb/100 is very (extremely?) high. The average seems to be around 60-65. I found one guy with ~10k hands and a SD of just 25 ptbb, but I can't accurately assess whether he's even a winning player. I still doubt that anyone maintains a CV of .25 in the long-run online at anything but the very lowest stakes.

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I know that for 3/6 LHE full ring on AP before they changed their bonus/rakeback/arp structure, it was entirely doable. My ratio was even better than .25. Their benefits added up to slightly better than 100% rakeback (which is why they changed it), adding up to between 2.25 and 2.5BB/100, and my winrate after 100k+ hands exceeded 2.5BB/100 at that level for full ring. And my Stdv/100 was less than 15BB/100. The ratio was close to .33.



You can do it at 5/10 and slightly above probably (after benefits), but only if you're extremely picky about which tables you sit at.