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8:53 pm
October 3, 2009
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Sean
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Let's say there are two poker players. Player 1 wins 10% of the time where he wins $28 for every $1 lost. Player 2 wins 70% of the time where he wins $1 for every $1 lost.
Which player would you rather be? Why?
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9:09 am
October 4, 2009
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Matt Flynn
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What's my bankroll? 
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9:31 am
October 4, 2009
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Sean
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Assume that each player is properly bankrolled for the given parameters.
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10:32 am
October 6, 2009
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robinnh
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Post edited 5:33 pm – October 6, 2009 by robinnh
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12:44 pm
October 13, 2009
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Hitman
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The guy winning 10% of the time, and it's not even close. Because he has a significantly higher long term win rate.
Matt's question is spot on, depending on br the 10% guy could have a very high risk of ruin, but if properly br'd such that the risk of ruin is not a concern, be that guy.
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3:15 pm
October 13, 2009
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Sean
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The player winning 70% will earn far more under a fixed fractional money management system.
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4:49 pm
October 14, 2009
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JJS
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This is an interesting problem. I did a simulation of these two players in an Excel spreadsheet assuming 500 betting rounds, and what I discovered is that if the players start with the same bankroll, and each player always bets the same fraction of his bankroll (say 1%) then player 1 (the player winning 10% of the time) will make more money faster than player 2.
However – and here's the rub – player 2 does not have to bet only 1%. His variance is much less and he can afford to bet a much larger fraction, as high as 15% without going bust in 500 rounds. If player 1 tries that, he runs a very big chance of going bust.
So… if we were to find the bet size for player 2 that gives him the same risk of ruin as player 1, I can see where it might be possible that player 2 will win more money faster than player 1. His bet size is larger, so he makes money faster.
I haven't actually done that calculation – you would have to figure out the variance of both players as well as each player's win rate, then do a risk of ruin analysis. I don't have the time to carry it that far, but anyway just going this far was very interesing.
I guess the moral of the story is, variance can be a killer – reduce it if you can!
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2:04 pm
October 26, 2009
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Hitman
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Sean said:
The player winning 70% will earn far more under a fixed fractional money management system.
A fixed fractional money management system is incongruent with poker, so I fail to see the point of your arguement.
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2:14 pm
October 26, 2009
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Hitman
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JJS said:
However – and here's the rub – player 2 does not have to bet only 1%. His variance is much less and he can afford to bet a much larger fraction, as high as 15% without going bust in 500 rounds. If player 1 tries that, he runs a very big chance of going bust.
JJS,
This is basically what the OP is trying to say with the fixed fractional money management system. The problem with this is that the betting limits are fixed (or capped) by the table stakes, so the 70% player can't realize the larger gains fractional risk increases would bring.
The OP's suggestion that fixed fractional money management would make the 70% player more profitable is akin to saying the 1-1 player is going to win more money than the 28-1 player because he plays $1000-$2000 and the 10% player plays $1-$2. Obviously.
I suppose the OP could make the arguement that the 70% player can move up in limits and sustain the new levels with no risk of ruin where as the 10% player would find that more problematic, but then the OP's original statement that each players is properly bankrolled removes that element imo.
If both players are already playing at the highest limit available, the 70% player doesn't stand a chance because he can't make the fractional increases required in a fractional money management system. The nature of the game having a ceiling on wager potential prevents it.
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3:31 pm
October 26, 2009
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Rich
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Hitman said:
Sean said:
The player winning 70% will earn far more under a fixed fractional money management system.
A fixed fractional money management system is incongruent with poker, so I fail to see the point of your arguement.
What is incongruent about constantly having 5% of your bankroll on a table?
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5:49 am
October 27, 2009
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Matt Flynn
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I didn't get back to this because it seemed straightforward: obv you choose the higher EV. But, I was assuming the games were same stakes, and that there weren't other stakes to choose from. With several stakes to choose from and adequate bankroll, this is a risk of ruin problem.
Soo, my guess is you have been studying the Kelly criterion. Plug and chug and let me know.
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5:10 pm
October 27, 2009
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JJS
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Matt – Were you referring to me? If so then I have to say that I really don't have the time to persue this any further than I already have. I was hoping that someone else would pick up the ball and let me know…
Hitman – I don't really disagree with anything you said. The fact is, the problem is not solvable as the OP stated it because we were not told what the constraints are.
If we assume that the players are already playing at the highest possible stakes, so bet sizes are constrained (you can't increase bet size because it is already at max) then as you say the 28-1 player will win much faster than the 1-1 player. The 28-1 player also needs a bigger bankroll than the 1-1 player when they both play at the same stakes.
OTOH if bankroll is the constraint, for example they both have the same not-terribly-large bankroll, then the 1-1 player could afford to play at higher stakes and (possibly) make more than the 28-1 player.
Anyway it's an interesting problem – it shows that EV isn't everything. You need to pay attention to variance too.
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2:01 pm
October 28, 2009
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Hitman
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Rich said:
Hitman said:
Sean said:
The player winning 70% will earn far more under a fixed fractional money management system.
A fixed fractional money management system is incongruent with poker, so I fail to see the point of your arguement.
What is incongruent about constantly having 5% of your bankroll on a table?
It's prevented by stake limitations at some point. Also, a fixed fractional money management system would not just require putting it on the table, it requires putting it in action… which is dependant on the amount your opponents have in action. For instance if you sat down at a table with 5% of your br, but your opponents only had 1/5th of that, then you're not really sitting with 5% of your br, you're sitting with effective stacks of 1% of your br.
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2:09 pm
October 28, 2009
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Hitman
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Matt Flynn said:
I didn't get back to this because it seemed straightforward: obv you choose the higher EV. But, I was assuming the games were same stakes, and that there weren't other stakes to choose from. With several stakes to choose from and adequate bankroll, this is a risk of ruin problem.
I was assuming the same thing Matt.
For the sake of argument, if an unlimited rise in stakes were possible, and full stack action at all stake levels available, which would allow for a fixed fractional money management system to be used effectively and indefinitely, the 70% 1-1 guy I believe would do better long term (assuming both players used the ffmms to avoid going broke) because the 70% guy would move up in limits consistently (all be it slowly), while the 10% guy would move up, experience high variance, and be required to move back down to adhere to the ffmms, making his ascent in limits more erratic and maybe even not possible long term. If the 10% guy broke from the system and attempted to stay in the higher limit moving up his risk of ruin shoots through the roof. I haven't done the math, just a guess.
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2:16 pm
October 28, 2009
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Hitman
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JJS said:
Anyway it's an interesting problem – it shows that EV isn't everything. You need to pay attention to variance too.
Very true in the real world. However the OP said to assume both are adequately br'd so risk of ruin isn't an issue… which when true, EV trumps variance.
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