Bankroll considerations based upon estimated edge and Kelly criterion?

I've been reading _Small Stakes Hold'em_ after having read a number of beginner low limit hold'em books. The recommended approach by Miller et. all is much looser and more aggressive. With those characteristics, I can envision much larger fluctuations over the long run. Assuming a solid understanding and implementation of SSHE approach, what kind of edge do you think you have against the average opponent SSHE was written to deal with, and are there any estimates in regards to standard deviation (in a nutshell, how large of downward fluctuations should someone expect on the way to long-term profits)? I had played Blackjack with an edge for a while, with some success, but the bankroll requirements for long-term success at BJ for a reasonable profit are steep given the common rules, table conditions and Casinos' suspicions of today. I would like to believe the bankroll expectations for long-term success against the current crop of (typical) poker players is not so lofty.

Post this in the probability section
Cheers

[bobbyi]

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Assuming a solid understanding and implementation of SSHE approach, what kind of edge do you think you have against the average opponent SSHE was written to deal with, and are there any estimates in regards to standard deviation (in a nutshell, how large of downward fluctuations should someone expect on the way to long-term profits)?

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Most (or at least many) people here studiously track all of their results at poker using software tools like Pokertracker (designed for online poker play) or Statking (designed for casino play). These programs automatically calculate standard deviation based on your results, so empirical values for typical games are pretty well understood.

I'm not sure what you mean by "edge". If you are looking for a percentage edge on the money wagered as I think people use in blackjack, that really is not a standard way of thinking about win rates in holdem. Much more common is to simply consider expectation (win rate) in terms of dollars (or bets) won per hour for live play. For online play, bets won per 100 hands is the standard.

To give you a rough feel of fluctuations and bankroll requirements, a typical win rate for a good player in a casino game is in the ballpark of one big bet per hour (e.g., $8/hr in a 4/8 game) and a typical standard deviation is roughly ten big bets per hour (e.g., $80/hr in the same 4/8 game). If you look through the archives, there have been discussions before about risk of ruin for various bankroll sizes, grapsh posted of random walks using these and other numbers and so forth. Conventional wisdom is that a reasonable bankroll is somewhere from 300 to 500 big bets for the game you are playing.

The Kelly criterion isn't used much by most poker players. The reason is that you can't really vary the size of your wagers while keeping everything else constant. Betting more requires playing in a higher stakes game which typically will feature much tougher players and different sorts of fluctations relative to the stakes, so there are often other considerations at work than simply how much money you want to be betting that are more important to deciding what to play.

Thanks for the helpful response.

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To give you a rough feel of fluctuations and bankroll requirements, a typical win rate for a good player in a casino game is in the ballpark of one big bet per hour (e.g., $8/hr in a 4/8 game) and a typical standard deviation is roughly ten big bets per hour (e.g., $80/hr in the same 4/8 game).

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I think this info can be turned into some meaningful estimates related to a Kelly-based bankroll; I strongly suspect the 300-500 BB recommendations came from a consideration of the formula.

[SNOWBALL138]

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I'm not sure what you mean by "edge". If you are looking for a percentage edge on the money wagered as I think people use in blackjack, that really is not a standard way of thinking about win rates in holdem. Much more common is to simply consider expectation (win rate) in terms of dollars (or bets) won per hour for live play. For online play, bets won per 100 hands is the standard.

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Just because it isn't the standard way of thinking about it doesn't mean it isn't a useful way of thinking about it. Barry G has some interesting discussion of percentage edge in his book. He talks about 1 BB per hour in terms of getting around 33bb worth of action per hour and having a 3% edge.

[TaintedRogue]

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Thanks for the helpful response.

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To give you a rough feel of fluctuations and bankroll requirements, a typical win rate for a good player in a casino game is in the ballpark of one big bet per hour (e.g., $8/hr in a 4/8 game) and a typical standard deviation is roughly ten big bets per hour (e.g., $80/hr in the same 4/8 game).

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I think this info can be turned into some meaningful estimates related to a Kelly-based bankroll; I strongly suspect the 300-500 BB recommendations came from a consideration of the formula.

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300*BB allows you to have 10 losing sessions of 2BB's pr hr over 10 8hr sessions and still have 140 BB left.

That's 10 losing sessions at 10/20 totaling 160BB/$3200 and leaving you a bankroll of $2800.00/140BB.

I really don't think it's possible for a good player to average that much of a loss over 10 sessions. Even if it's so, he has over 1/2 his bankroll left.

I'm talking 1 table live poker here.

Nice to see other Blackjack AP's here.
-Shaggy

[xxx]

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I'm not sure what you mean by "edge". If you are looking for a percentage edge on the money wagered as I think people use in blackjack, that really is not a standard way of thinking about win rates in holdem. Much more common is to simply consider expectation (win rate) in terms of dollars (or bets) won per hour for live play. For online play, bets won per 100 hands is the standard.

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Just because it isn't the standard way of thinking about it doesn't mean it isn't a useful way of thinking about it. Barry G has some interesting discussion of percentage edge in his book. He talks about 1 BB per hour in terms of getting around 33bb worth of action per hour and having a 3% edge.

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It's amazing- I was thinking about this when I woke up this morning, came to make a post, and see the topic under consideration.

Assuming:
A 3% advantage (1bb/33 big bets in action per hour)
5 played hands an hour (30 hands * 0.2 for a tight player including some free looks in the big blind)
And the Kelly criteria
gives:

big bets per played hand = (33/6) =6.6
Optimum bankroll for fastest bankroll growth= 6.6/0.03=220 bb

(This assumes a bankroll resizing between hands)

Does anyone see any flaws in the argument? I may try a quick OIC based on this criteria.

To the OP: blackjack has a huge bankroll requirement because of the tiny edge- this is one huge advantage of poker if you get in a good game.

[SNOWBALL138]

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(This assumes a bankroll resizing between hands)

Does anyone see any flaws in the argument? I may try a quick OIC based on this criteria.



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Practically speaking, any bankroll that can be "resized" indefinitely doesn't need to worry about kelly betting. Wouldn't it be more correct to say that the betting is resized so that each bb is a 1/220th of the bankroll?

[xxx]

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(This assumes a bankroll resizing between hands)

Does anyone see any flaws in the argument? I may try a quick OIC based on this criteria.



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Practically speaking, any bankroll that can be "resized" indefinitely doesn't need to worry about kelly betting. Wouldn't it be more correct to say that the betting is resized so that each bb is a 1/220th of the bankroll?

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Yep, that is what I was trying to say. Just got my words twisted around a little when writing the post.