I apolagize if this has been discussed before...

But here it goes: While reading a discussion about NL vs. Limit, I read that Zach wrote, "EDIT - Just a note on the fact that everyone calls down. This will greatly increase your variance,it out as you will suffer more "bad beats", but you will win in the long run with donks calling down."

I've been thinking about variance a little bit recently, but i don't know enough about Stats to come to any resonable conclusions by myself.

Basically my question is will the swings be worse in a game filled with better players (so there should be fewer bad beats), where your win rate is only 1BB/100 or will the swings be worse in a loose game filled with bad players who frequently put beats on you, but you are beating the loose game for 2BB/100?

I have no mathematical basis to back that up.

My assumptions however is that Standard Deviation is a function of, among other things, pot size and % to the flop.

Your winrate is a far more important figure. It varies much more (proportionatey) than your variance ever will. You can double or triple your winrate by playing in loose/passive games, and your stdv will go up by maybe 5-10%. If that's something you look to avoid, you probably arent winning to begin with.


A 1BB/100 winner with a 14BB/100 stdv is going to experience more "swings" than a 2BB/100 winner with a 16BB/100 stdv.

I would argue that 2 bb/100 winner would in fact experience more swings. However, those big swings are more likely to be up. The 1 bb/100 winner certainly has more downside risk, which is all that really matters.

Zach is correct.

Let's say you have bottom set on a 2-suited board with a str draw.

You check OOP and first opponent bets, 2nd opponent calls. Let's say you are super weak and now you "fear someone may have an over set" and you just call.

If you push here there are two outcomes assuming both of your opponents has the draw:

1. You win
2. Someone calls with their draw

It's silly to have to say, but when you win you have 100% equity of the pot. It's yours.

If someone calls with their draw you'll have 75-80% of the equity. Which brings more equity, i.e. which has less variance? It's clear I hope

So if you just call down you are getting exactly your pot equity. Against an OESFD you will win roughly 2/3 of the time. Whereas if you push you win %TIMES_OPPONENT_FOLDS + %EQUITY_WHEN_OPPONENTS_CALL which is greater than just your pot equity.

This doesn't say anything about $WON, but it does say a lot about variance.

Playing fast lowers variance. Calling down increases variance.

Bad players are also more passive.

Passive play means smaller pots.