Quote:
Originally Posted by Simpletwn
EV has nothing to do with variance as it'll always be somewhat subjective (we need to know villain's exact range in each spot, a solver's EV makes all types of assumptions as well).
In statistics variance is expressed in stdv, and then there are confidence intervals etc, so the guys in this thread are right but they're just being particular for arguments sake and not to answer your question...
If we classify variance as the thing we are actually interested in as poker players.... ie, the likelihood to swing in any certain direction, duration of downswings etc then variance is determined by standard deviation and actually more so, your winrate, which affects your confidence interval.
Standard deviation is determined by the size of the pots you play for (the bigger the pots, the bigger the possible swings) winrate is determined by skill of course.
Players with a 10bb/100 WR and 120 stdv will still experience less variance than players with a 1bb/100 winrate and 75 stdv. The latter can actually lose over a million hands due to variance.
Try this to test https://www.primedope.com/poker-variance-calculator/
No, you do need EV to calculate variance, whether it’s over multiple hands or a single hand. Over multiple hands, variance is a measure of the divergence of your actual results from your true win rate. But what is your true win rate? That’s just the sum of the EVs of each individual hand you play, so EV is still needed to determine variance.
And it’s not true that the player with the 10BB/100 win rate and 120 sd has less variance than the 1BB/100, 75 stdv player. The 1BB/100 player is certainly more likely to suffer downswings, but the 10 bb/100 player will see more and larger divergences from his 10BB/100 win rate — that’s what the higher variance means. Variance is NOT a measure of how likely you are to experience a negative result. It’s simply a measure of the difference between actual outcomes and the expected value of that outcome.
Minimizing variance seems to be something many regard as a positive thing, but that is really not the case. In your example, which stats would you rather have, the 10BB/100 with higher variance or the 1BB/100 with lower variance? The answer should be obvious. How do you get the higher win rate? Obviously by making more +EV plays in hands, regardless of whether they increase variance or not.
If you REALLY want to minimize variance, that’s easy — just fold every hand. The variance of folding is zero; there’s no possibility of different outcomes if you fold PF. Your EV is either 0, -0.5, or -1 bb (depending on your position), and you will realize that outcome every time. Obviously that’s not a profitable way to play poker, though.