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Texas Hold'em No Limit Intermediate

Microstakes Myth 2: Variance mainly applies to higher-stakes

6,804 Views on 16/1/12

It's not a low-variance level. There' just as much variance at the micros, if not more!

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Variance may even be higher at the microstakes, even more of a reason to play solid fundamental poker.

This myth arises due to a misunderstanding of the relationship between variance and your winrate  (assuming winrate is inversely proportional to how difficult the games are). Variance and winrate are NOT directly proportional (even though some correlation may be observed in certain cases)

Someone might beat a micro-stakes at a nice winrate, and assume because they are winning at a nice rate that it is "low variance". When they break even at a higher stake (and tougher game) they may assume the higher stake game entailed more variance which is why they are not winning as much.

In actuality variance operates independantly of win-rate. The standard deviation (the square-root of variance) is a measurement of how big the average deviation from our expected winrate is. If our standard deviation is 0, it would mean we always ran exactly at our winrate. It is therefore completely possible to have a low winrate with low-variance style and a high winrate with a high variance style etc.

If we were to examine the relationship between variance and winrate across a variety of stakes it would perhaps look something like this graphic.

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Even though variance at the micros is high, your expected value is huge!

Noticepokerimage that initially variance drops as you progress from micros to small stakes. There are less players making high variance plays such as chasing draws. These are high-variance plays because you either win a big pot, or lose a big pot. Your EV is actually higher when bad players do chase draws with low equity, but your variance is also higher, because when you do lose, you lose a bigger pot.

If you compare this to a slightly higher stakes game (maybe lower small stakes), a slightly better player might fold his marginal draw; which has a lower EV for hero, but also entails less variance. Hero wins a slightly smaller pot more often.

If we  consider another possible scenario at even higher stakes , the competent players might start shoving their marginal draws over cbets or turn-barrels. This makes the game both lower EV for hero, AND higher variance.

Why is variance so high at the highest stakes?

To capitalise on the ever decreasing edges at the high/nosebleed stakes, players are forced to make higher variance plays. We can hence see some inverse correlation between variance/winrate towards the higher stakes, but this is circumstantial rather than a result of them being inversely proportional. It's of course, completely possible to play a very low variance style at high stakes; it just might result in you losing when you are exploited too heavily.

Also plotted on the graph is  an indication of the "sweetspot" theory. Variance is at its lowest, and the decline in winrate plateaus due to less "fuzziness" when estimating hand-ranges.

Hopefully we can see that not only is variance still relevant at the micros, but since variance is NOT a function of winrate, variance at the micros may even be higher than the variance at some small stakes games.

Author

w34z3l

I am of British nationality and go by the online alias w34z3l. I am considered one of the top consultants in the field for technical analysis (i.e. database work) and application of game theory concepts to various card games. I make a ... Read More

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