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Old 10-08-2018, 12:15 PM   #1
DottMySaviour
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Question How can I apply Kelly criterion in cash games?

Let's say I know my BB/hand is 0.1 (10BB/100hand), I buy-in at 100BB, I leave the table when I'm at 200BB. Can I apply Kelly criterion to find out my optimal bankroll with only these information? If not, what information do I need?

Is there any maths genius out there who can help me with this question?
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Old 10-08-2018, 02:19 PM   #2
alkimia
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Re: How can I apply Kelly criterion in cash games?

Quote:
Originally Posted by DottMySaviour View Post
Let's say I know my BB/hand is 0.1 (10BB/100hand), I buy-in at 100BB, I leave the table when I'm at 200BB. Can I apply Kelly criterion to find out my optimal bankroll with only these information? If not, what information do I need?

Is there any maths genius out there who can help me with this question?
I'm not really sure if kelly would apply and if it does I'm not sure if the way I've done it makes much sense but I'm a huge math nerd and this interested me.

So a win rate of 10bb/100 shows an average win rate but the calc for kelly needs different information. One way could be to look at your database in chunks of 100x hands(I label a session from here on out).

the kelly formula is: W – [(1 – W) / R]

Where:
W = Winning probability
R = Win/loss ratio

The process could be:
W: count your 100x hand sessions and take the winning sessions divided by the total sessions
R: divide the average gain in winning sessions by average loss in losing sessions

This would give you the optimal amount of your bankroll to risk on any one 100x hand session. Again I'm not really sure if my logic is right and if it is I'm not really sure how useful that would be.
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Old 10-08-2018, 03:04 PM   #3
alkimia
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Re: How can I apply Kelly criterion in cash games?

I don't have my database currently available for me to test this so I just worked backwards using some standard numbers. Lets assume 56% winning sessions and a 10bb/100 hand win rate. With those numbers we can estimate the win/loss ratio by doing (win percentage * average win) - (lose percentage * average loss) = average expected win(10bb/100 in our case). E.G (0.56*50)-(0.44*40.9)=~10bb/100. The win loss ratio given that example would be: (50/40.9)=1.22. Making the kelly forumal: 0.56-(0.44/1.22)=0.199 or 19.9% which seems excessive to me.

Last edited by alkimia; 10-08-2018 at 03:17 PM.
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Old 10-08-2018, 03:14 PM   #4
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Re: How can I apply Kelly criterion in cash games?

Here is a better example than the one I posted:

https://forumserver.twoplustwo.com/s...36&postcount=5
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Old 10-08-2018, 04:43 PM   #5
browni3141
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Re: How can I apply Kelly criterion in cash games?

Kelly criterion is not well suited for poker because of a discrete set of bet sizings (nothing inbetween 1|2 and 2|5), the wide range of possible results for a given hand, and the fact that poker is not scalable. Higher stakes get tougher.

For bets with multiple outcomes, use edge/variance to estimate the fraction of your bankroll to bet. For example, pokertracker might say you have an edge of .1BB/hand and a standard deviation of 10BB/hand. This means you should bet .1/10^2 = 1/1000 of your bankroll. 1000BB is the optimal bankroll amount at the stake you wish to play.
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Old 10-08-2018, 04:44 PM   #6
alkimia
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Re: How can I apply Kelly criterion in cash games?

Quote:
Originally Posted by alkimia View Post
I don't have my database currently available for me to test this so I just worked backwards using some standard numbers. Lets assume 56% winning sessions and a 10bb/100 hand win rate. With those numbers we can estimate the win/loss ratio by doing (win percentage * average win) - (lose percentage * average loss) = average expected win(10bb/100 in our case). E.G (0.56*50)-(0.44*40.9)=~10bb/100. The win loss ratio given that example would be: (50/40.9)=1.22. Making the kelly forumal: 0.56-(0.44/1.22)=0.199 or 19.9% which seems excessive to me.

I looked at this a little more in depth as well as looked over the link I posted above. The variance in your sessions(or win/loss caps) is key to getting the correct percentage out of the kelly formula. So lets take the following example average wins/losses in bb for 100x hands


Code:
A) win=200, lose=230: (0.56*200)-(0.44*230)=~10bb/100
  0.56-(0.44/(200/230))=0.054 or 5.4%
B) win=100, lose=104.5: (0.56*100)-(0.44*104.5)=~10bb/100
  0.56-(0.44/(100/104.5))=0.1 or 10%
C) win=50, lose=40.9:(0.56*50)-(0.44*40.9)=10bb/100
  0.56-(0.44/(50/40.9))=0.2 or 20%
Most professional sports bettors would tell you that using the kelly criterion can lead to you going broke and would recommend that you use half of that or less.
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Old 10-09-2018, 04:54 PM   #7
pucmo
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Re: How can I apply Kelly criterion in cash games?

I think blackjack has stuff about that subject and it is mostly about the big bets you make.

I can simply think about the effective stacks or just my 100 bb and think every stack of mine has an over 50% chance of winning (heads up or perhaps not given enough time). Then you will be flipping and flipping, winning some money every time on average. The chance of losing or doubling X stacks.
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Old 10-11-2018, 04:32 AM   #8
ohly
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Re: How can I apply Kelly criterion in cash games?

Cash: Everything written here is valid for cash as well, except you should take the winrate in ptbb/100 as ROI and (SD/100)^2 as variance. However, B is not the variable you will be after. A better formula is R = variance / ROI * 2, (that's R = variance / ROI * 4 for ½ Kelly), where R is the size of your roll in big blinds.

https://forumserver.twoplustwo.com/1...ah-brm-884641/
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