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 Originally Posted by Renton
Yeah that's certainly what I'm looking for, assuming it is correct.
I agree with JV's numbers.
Originally Posted by Renton
Now I want to figure out how to quickly do this for a variety of % ranges i.e. 99 90 75 etc, and manipulate the population a little and see what results.
This is gonna be an easy task.
The multiplicative factor of 1.92 is the only thing that changes when you're looking at different CI %-ages. For simplicity, I'm going to use the "infinite trials" value, which should only have a slight error in the 3rd sig.fig.
75% CI -> 1.15
90% CI -> 1.64
95% CI -> 1.96
99% CI -> 2.58
On Excel, you can get this number by putting the %-age in cell A1. Into another cell, enter
=NORMSINV(1-(1-A1)/2)
Originally Posted by Renton
For example if we change our equity on the river from 33% to 37%, how much different do those numbers look? I'm gonna set up a google sheet for this.
Well, first off, if your equity goes from 33% to 37% and the bet sizes remain the same, then the EV will be positive. We know that 33% equity is exactly break-even with those bet amounts. So greater equity means greater EV, and EV was 0, so def. +EV.
Originally Posted by Renton
My end goal is to test a hypothesis that I have which is the following: Very thin plays for big bets aren't just marginally +EV, they're -EV.
No matter how wide the variance, if a bet is +EV, then the expectation is to win more than is lost after many bets.
Originally Posted by Renton
Practically, at the sample sizes humans are capable of experiencing, particularly during reasonable spans of time (say around 6 to 24 months of play), if you can't be reasonably confident that the play will result in equity > the mean, and your bankroll and sanity aren't nearly infinite, you should just pass on these spots. So I want to know "how thin is okay" for a variety of common poker situations, and eventually develop an intuitive sense of this.
We know that all +EV bets are good in the long term, but sanity has time constraints. I feel like the obv answer is if you want to take poker seriously, you have to embrace the variance, not avoid it. The assumed goal is to seek out the max EV in any situation, even if a lower EV play has lower variance.
I'm interested in your conclusions.
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