kelly criterion

[chok1]

ive read a few differnet articles and threads about bankroll, win rate, standard deviation, and kelly criterion. how do these concepts apply to the poker game at hand. Is this what jesus ferguson was using when he was talking about how he turned one dollar into 20,000?

[AlanBostick]

Bankroll management concepts don't particularly apply to the play of individual poker hands, or even the metagame within one particular session. Bankroll management comes into play in decisions of whether or not to sit down in a particular game.

In effect, in Kelly-betting terms, the "bet" one makes is one's buy-in when one sits down in a particular game. A Kelly-betting poker player is going to play in a game with betting limits that maximize the player's rate of growth of her bankroll.

It turns out, by the way, that the rule of thumb of requiring a bankroll of 300 big bets to play in a game corresponds to a "typical" winning player wagering with a Kelly criterion of 0.3, a value frequently held to be a good compromise between bankroll growth and protection from ruin.

[pzhon]

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Bankroll management concepts don't particularly apply to the play of individual poker hands,

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Actually, they can, as was discussed in a past article in the Two Plus Two Internet Magazine. If you are sure that you have a pure gutshot draw and no chance to win otherwise, bankroll considerations may increase the pot odds you need to call slightly.

In practice, this is tough to use. Most players are bad at recognizing exactly which situations are marginal, and may give up safely profitable gambles in the name of variance reduction.

[BillC]

The concept is a more precise version of the advice that one should forgo marginal +EV, high SD situatons. So for example if you have a longshot draw, you need slightly higher pot odds than dictated by pure EV. There are plenty of situations where this kicks in cleanly and the math is pretty clear. E.g. all-in situations where there are no implied odds. For draws with 1 or 2 outs, the effect is quite significant.

BillC

[AaronBrown]

Before Kelly, most people would have said that taking more risk increases your chance of both very good and very bad outcomes. From a conceptual point of view, the most valuable insight Kelly had is that is not true. More risk always increases your chance of very bad outcomes, but beyond a certain point it decreases your chance of very good outcomes as well. In that sense, the Kelly criterion gives the upper limit of risk anyone should consider. Beyond that point you lose more from the chance of going broke, and thereby missing out on future positive EV opportunities, than you can gain from bigger wins when you win.

[SoothSabre]

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In effect, in Kelly-betting terms, the "bet" one makes is one's buy-in when one sits down in a particular game. A Kelly-betting poker player is going to play in a game with betting limits that maximize the player's rate of growth of her bankroll.


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You use the phrase "buy-in". Is there a difference in ROI / Risk of Ruin based on similar buy-ins but with different limits ? In other words, does a good player maximize bankroll growth by:

sitting down with $400 (100% of max allowed) at 2/4 NL

OR

sitting down with $400 (40% of max allowed) at 5/10 NL

I realize variance would be much higher but am using the assumption that player is adequately bankrolled.

Thanks in advance.

[Shroomy]

The Kelly principle doesnt relate as well to poker as it does to other games (black jack especially!)

but kelly would say that you should figure out your estimated edge for a particular game and only wager the percent of your bankroll in proportion to your edge.

so if you lost you would move down in stakes and if you won (if you projected your edge correctly you should eventually) you would move up in stakes.

of course this doesnt take into account the different skill levels of opponents at the the different stake levels.

All in all kelly doesnt relate well to poker in specific, but to maximizing return w/risk in general.

And remember if you follow it perfectly you are still going to have a 50% chance of losing 50% of your bankroll at any given time.

[Mr. Now]

Shroomy,

Thank you for your post.

Kelly is used to determine optimal bet size. It is a risk sizing/position sizing method and procedure. It is in fact "fixed fraction money management".

Mr. Now notes that the best money management procedure in the world can, at best, only delay the inevitable day of ruin if you strategy does not have +EV.

Money management does not, and cannot, replace a strategy that generates +EV spots to place bets.

Thus poker theory and effective strategy are essential, and money management is merely helpful, but only to the extent you already have +EV strategy and tactics in place.

[jjpokertime]

Kelly doesn't really deal with the poker hand in play but with your bankroll and how the size of your bets affects it.

Kelly is about investing and how much it takes to invest safely. Kelly providess way to numerically analyze your "Risk of Ruin", "Probablility of success", "Probability of Survival", and "Risk of Ruin before goal" the data is in percentages.

Since investments fluctuate positive and negative you must be able to suffer losses to attain gains.

So for poker you should not play in stakes above your bankroll. (Ie. You can't play a 10/20 with $20 dollars one hand and you are all in with no chance to manuever or outplay your opponent.)

The correct size is about 600 max bets in Poker games. This is lower than blackjack because of the lack of uncertainity about the variables (used to complete the percentages): r (big bets/ hour) and s (standard deviation). More money is safer. this provides you with a Kelly value or Kelly fraction of k=1/6. This is conservative but due to the nature of poker it is a safe play. If a losing streak of 100 big bets occurs you should move to a lower level to protect your bankroll.

But kelly teaches you an important lesson. The less you risk the harder it is to reach your goal. and subsequently the more you wager the greater your risk of ruin.

Using kelly will mazimize your chances of seeking a positive return before you go broke. Futures traders use Kelly to limit their risks and to insure they won't go broke if there is a bad streak in the market. Being able to weather a storm to reach their goal.

you can read more about Kelly in blackjack forums such as stanford wongs site at www.bj21.com and www.bjmath.com the later goes into all the details to crunch the numbers yourself. Uderstanding kelly is essential to win at blackjack, and protect your bankroll in poker from going bust.

[pzhon]

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The correct size is about 600 max bets in Poker games. ... this provides you with a Kelly value or Kelly fraction of k=1/6.

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You are making a lot of questionable assumptions.

[img]/images/graemlins/diamond.gif[/img] You are assuming a particular win rate (or win rate/variance). Some games are softer than others. An expert playing in a tough $150-$300 game can't expect to win at the same rate as an expert playing in a soft $2-$4 game.

[img]/images/graemlins/diamond.gif[/img] Many winning players are only marginal winners. Marginal winners may need more than 600 BB to be as safe as an expert would be with 200 BB. Losing players are not safe with any amount.

[img]/images/graemlins/diamond.gif[/img] A Kelly fraction of 1/6 might be great for you. It might be ridiculously conservative for someone else. The appropriate Kelly fraction to use depends on your personal risk tolerance and ability/willingness to move down or up.

Maybe the inaccuracies in these assumptions will cancel, and maybe they won't. Tossing out yet another number without context is not progress.

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The less you risk the harder it is to reach your goal. and subsequently the more you wager the greater your risk of ruin.

Using kelly will mazimize your chances of seeking a positive return before you go broke.

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No, it won't. If you don't care how rapidly you win, but want to maximize the probability of showing a particular gain, you should bet less than the Kelly Criterion recommends (or even a Kelly fraction of 1/6).

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Kelly doesn't really deal with the poker hand in play

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In theory, it is applicable, as was mentioned elsewhere on this thread. However, most players are not good at identifying which situations are really marginal.

Suppose you are considering playing a hand that has a standard deviation of about 3 BB, and an expected return of about 0.1 BB. The Kelly Criterion says you are betting the optimal fraction of your bankroll if your bankroll is about 3^2/0.1 = 90 BB. The Kelly Criterion recommends accepting the opportunity if your bankroll is at least about half of this, 45 BB, or k*45 BB if you use Kelly fraction 1/k. This is safer than playing normal poker, so if you have the bankroll to play in the game in the first place, you should play the hand, and it's not close.