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.

It’s amazing how well players can play when they are playing well and winning versus how poorly they play when they are not.  I have a lot more to say on this in another, but for now, its off to work!

There is usually a fine line between costing yourself too much expected value in the present term in order to expand your range to gain yourself more expected value in the long term.  I see far too many players against whom it is difficult to narrow down their range, but because their range is so wide, solid play defeats them.  For example, if someone pushed all in every hand, they would be unreadable and their hand range would be wide, but it would be very easy to beat an opponent who plays like that.

Let me show you two examples where narrow hand ranges played a role in allowing me to win a pot I would not have ordinarily won.

Playing $5/$10 No limit with $2500 effective stacks.

There are 5 limpers and I call out of the small blind with 98o.  The flop comes Jh7s5s giving me an open ended straight draw.  I check, the big blind, who is a solid regular bets $50.  3 players call and I call as well.  The turn is the Tc.  I lead out $175 and the big blind makes it $675.  Everyone else folds and I am 100% sure that he has the straight here.  Because he is limited to only having the nut straight here (he wouldn’t raise 2 pair with so many people to act behind him, and wouldn’t bet the flop with 43 into so many people) we are currently splitting the pot.  However, I can make it look like I have something else so that if a scary card comes on the river, I can bet and hopefully win the pot.  Note how his limited range should allow me to play perfectly against him, while he has a more difficult time playing against me.

I elect to call and the best card comes on the river, the Js, bringing in the flush draw and pairing the board.  I elect to shove all in and he grumbles about it being the worst card for the straight and folds.  If he had a wider range then just the nuts on the turn(or if I thought he might have a wider range), then I would not have been able to play optimally against him and would have just shoved all in on the turn to with the hopes that he would call with a worse hand, or fold his equity in the pot.

Another example comes from pot limit omaha(in this game you MUST play 2 cards from your hand).  Effective stacks are $700.

There are 2 limpers and I complete the small blind with 8c7c7s6s. The flop comes Jc9d7d.  I bet $20 and only the big blind calls.  I have played with him a bunch and know that he will only put a lot of money in with the nuts and will not be tricky.

The turn is a 4c giving me a flush draw along with bottom set.  I bet $60 and the big blind calls.  My plan is to bet a river that does not pair the board or complete a flush just in case he has a bigger set.  Since I am representing T8 for the straight(and can easily have it), and I know he will never call the turn with the nuts or call the river without it, my bet is what I call a freeroll.  I am rarely beat by a better hand, but just in case I am, I will win the pot anyways.

The river is the 2s, completing no draws.  I bet the pot and the villain throws up his hands in disgust, shows me JJQT which had me in very bad shape, and folds it.  If my opponent was tricky in this situation and could have just called with the nuts on the turn so that HE could win the pot if the board changed, then I would have had a lot more concern about betting the river(and the turn too).  In this case, my opponents straightforward play caused him to lose a pot that another opponent might have won.