DrStrange
4 of a Kind
In limit games, the typical win rates for "good" players is small relative to variation. A good limit player is winning 2BB per 100 hands while the standard deviation is ~~13BB per 100 hands. Luck has a much greater effect here. And tiny mistakes can cripple win rates. This sort of game birthed the notion that it can take tens of thousands of hands to begin grasping the difference between how good a player is and how lucky/unlucky they are.
Win rates in big bet games often are much higher than variance. My win rate was something like 15bb to 20bb per hour, and I wasn't the best player in the game most nights. The standard deviation was 17bb per hour.
No doubt each of our games will be a little different. Even so, the math remains similar. Any given hour, the variance and win rates are similar in size. But the win rate scales ratablly, you get an average of 15bb per hour for each hour played. But the standard deviation scales with square root of the number of hands played / hours played.
Play a hundred hours, win an expected (100 X 15bb) = 1,500bb. Play a hundred hours and the standard deviation is SQR(100) X 17bb = 170bb. You will note that the 1,500bb win rate is much larger than the 170bb variance. The chance of a solid winning player who should be winning 1,500bb over a hundred hours actually losing is essentially zero - it is more than eight standard deviations from the expected value.
So many words to say that Hero true win rate has been crippled if he is losing money after playing for a hundred hours and losing. This isn't bad luck. This isn't run bad.
Caveats - - - Maybe hero's base win rate is much lower than 15bb per hour? If the win rate is barely better than breakeven then luck will run rampant just like a limit game. Maybe Hero's sample size is tiny, say fifteen hours or less? Could be the ultra-deep stacked game led to a tiny handful of disaster hands. Lots we don't know.
But, if Hero has been raking in big wins for all of 2020 - 2022 and now the last few months have been losses, that means something is going wrong with Hero's game and/or some new shark(s) is taking Hero to the cleaners.
Hate to be a doom sayer, but here it is -=- DrStrange
PS By the way - if the weak players are willing stack off with hands worse than TP/TK Hero should accommodate them. Waiting for the near nuts leaves a lot of value on the table. Variance is higher but so is the win rate.
Win rates in big bet games often are much higher than variance. My win rate was something like 15bb to 20bb per hour, and I wasn't the best player in the game most nights. The standard deviation was 17bb per hour.
No doubt each of our games will be a little different. Even so, the math remains similar. Any given hour, the variance and win rates are similar in size. But the win rate scales ratablly, you get an average of 15bb per hour for each hour played. But the standard deviation scales with square root of the number of hands played / hours played.
Play a hundred hours, win an expected (100 X 15bb) = 1,500bb. Play a hundred hours and the standard deviation is SQR(100) X 17bb = 170bb. You will note that the 1,500bb win rate is much larger than the 170bb variance. The chance of a solid winning player who should be winning 1,500bb over a hundred hours actually losing is essentially zero - it is more than eight standard deviations from the expected value.
So many words to say that Hero true win rate has been crippled if he is losing money after playing for a hundred hours and losing. This isn't bad luck. This isn't run bad.
Caveats - - - Maybe hero's base win rate is much lower than 15bb per hour? If the win rate is barely better than breakeven then luck will run rampant just like a limit game. Maybe Hero's sample size is tiny, say fifteen hours or less? Could be the ultra-deep stacked game led to a tiny handful of disaster hands. Lots we don't know.
But, if Hero has been raking in big wins for all of 2020 - 2022 and now the last few months have been losses, that means something is going wrong with Hero's game and/or some new shark(s) is taking Hero to the cleaners.
Hate to be a doom sayer, but here it is -=- DrStrange
PS By the way - if the weak players are willing stack off with hands worse than TP/TK Hero should accommodate them. Waiting for the near nuts leaves a lot of value on the table. Variance is higher but so is the win rate.