# The Final Word on Variance, Winrates, Small Edges and Loose Aggressive Players

In this post, I want to explain how variance, your winrate, pushing small edges and being a loose aggressive player come together to affect your winrate and your game.

There are two definitions of variance.  The first is the statistical definition of how far a set of numbers is from their mean.  For example, if you were a conservative player(tending to play less hands) winning \$100 an hour playing poker, your variance would be lower than someone who was a more aggressive player (tending to play more hands and be involved in more pots).  The reason is that there are more opportunities for your stack to go up and down as you are involved in more pots.  The other definition of variance used in the poker world is the idea that all situations will even out in the end, so that being on the wrong end of a bad situation is just “variance,” or a statistical anomaly taking focus away from what is really important aka. your winrate.  So when you have KK and the other person has AA, you can usually chalk it up to “bad variance” meaning that it was unlucky and that if the situation was reversed, the outcome would be the same.

In theory, if your winrate was high enough and your variance low enough, you would never(or at least very, very rarely lose).  For example, if your standard deviation(the square root of variance) was \$20 an hour, your winrate was \$100 and your results were normally distributed, you would only lose when you had a result that was 5 standard deviations away from the mean(which is about 1 in 1.7 million).  The reality is no one has a high enough winrate and low enough variance to never lose(or come close to it)  and that results are not normally distributed.  I was one of the most successful players in midstakes no limit and my winrate was approximately 5.5 big blinds per hundred hands and my standard deviation was approximately 65 big blinds per hundred hands.  Although I frequently lost during an individual hour, I won approximately 70% of the days that I played and 100% of the weeks.

When I hear other players talking about going through a prolonged losing streak(aka a “downswing”) they are often focused on the second kind of variance, instead of the first kind.   They often fail to realize that the main culprit for their losing money is not having a high enough winrate(or too high a variance).  For example, if two players have the same standard deviation (the square root of variance), say \$70 an hour, and one wins at \$100 an hour and one wins at \$30 an hour.  When they both experience a rough patch and are one standard deviation away from their results, the player winning at \$30 per hour loses \$40 an hour during this period and experiences a “downswing,” while the the player winning \$100 wins only \$30 an hour during this period.  However, they are both the same dollar amount and standard deviation from their true results!

Why should I care about all of these statistics and numbers you ask?  The answer is simple, poker is an emotional, thought driven game and results and emotions can affect the way you make decisions .  I assure you that the player who has undergone a “losing streak” takes it much harder mentally and emotionally than the player who is still winning, albeit at a lower rate.  If you feel like you have been losing and that the plays you have been making have not been working, you are less likely to make the optimal play when the opportunity arises.

It has been proven that losses hurt twice as much as wins thrill.  This idea is very important when comparing more conservative and aggressive playing styles.  As a looser player it is much tougher to maintain your winrate because when you are losing it is tougher to play your A game AND you are involved in more situations.  Not only does losing cause you to play your B or even C game, where your decision making is worse, as a looser player, you are now making more of those bad decisions.

When playing poker in person, you get the opportunity to observe people for large amounts of time and you can see there are many players(often of the loose aggressive variety) who do very well when winning, but who, when losing, play the same way despite the fact that their edge is no longer there.  For example, let’s say it is profitable to open T3s on the button when everyone has folded.  Doing so requires that you value bet 2nd pair well, fold when someone has a bigger flush, call at the right time with draws and a host of other things.  When a loose aggressive player is playing well and winning, he might be able to do all of these things and to turn a profit.  However when he is not playing well, playing this hand might get him into situations where his errors compound and he is no longer able to make all of the correct decisions necessary to make this hand profitable.  If he continues to lose, his winrate will drop, he will win less frequently and play less than his A game more frequently, all of which will contribute to less winning and more frustration.

There are many reasons that it might be beneficial to play tighter, but I believe that the most important one is the reduction of your variance.  Since many players do not have an adequate bankroll to play in the stakes they normally play, increasing variance and lowering their winrate increases the risk of ruin if they happen to encounter a run of bad variance.  This will prevent otherwise winning players from being able to play(and therefore win) assuming they could always play their A game, which is a near impossibility when they are losing and low on funds.  Playing more conservatively will allow you to play your A game longer, since you will be winning more instead of losing.  In addition, playing tighter has the huge benefit of helping you to avoid situations that are close that will tend to become unprofitable if you are not playing your A game.

The end result is that reducing your variance and keeping your winrate high has important additional benefits like keeping your mind sharp and being in the positive frame of mind that will allow you to win even more money.

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