Small Edges and Bankroll Growth

[ACW]

This sounds the wrong way round to me. I think that reducing macro variance can be important, but that reducing micro variance never is.

[O Doyle Rules]

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In the micro view I am always looking for ways to minimize variance if the cost in EV is not too high. In poker there are many ways in which you can trade off one against the other.

For me, if I lower my variance in the micro view I can actually raise my EV in the macro view. Less volatile swings in a game means I'm more relaxed, I'm less likely to tilt, I play better and I can play longer. And the most important reason is that I can play at a much higher limit.

So, less EV per hand can actually be more EV overall.

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I think this is a valid point. For certain individuals, a lower variance style of play perhaps could be +EV just for them due to their emotional makeup and their ability or inability to handle large bankroll swings.

I know my climb through the limits (online play) from .50/100 thru 3/6 was a steady profitable one by playing closer to a Lee Jone's style of play (look for a reason to fold) and this was for a large sample of hands.(>350k hands)

My results since switching to a SSH style of play has been much more volatile, and less profitable. (approx. 150k hands)

Assuming that I employed both styles of play to the same level of correctness, (I know there is no way I was playing either style 100% correctly) I am starting to feel that "just for me" (and maybe certain other players) that a lower variance style of play might in fact be better for their "peace of mind" when playing poker and therefore more profitable for them longterm.

[alThor]

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Until a few years ago, it was thought that a good BJ player should push small edges ... A smart fellow, Karl Janacek, showed that such plays actually slow bankroll growth because of increased variance.

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Just for the record, these ideas (Kelly) were known over 50 years ago. If you want bj-specific references, start with Joel Friedman's risk-aversion article, which was published in 1980 (a couple years after KJ was born).

alThor

[Paul2432]

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Nonetheless, David Sklansky has sort of written about this topic, although I forget exactly where.

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Take a look at this post from RGP . Sklansky says:

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Some of the big players have an incorrect opinion because when I do step up to 300-600, I do so because I feel that the game is good enough that a very tight, sub optimum strategy, will still result in a high hourly rate while maintaining a low SD.

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Paul

[2ndGoat]

Argument 1) Individually Positive EV plays can slow geometric bankroll growth.
Argument 2) Altering your play to reduce variance is a can of worms.

I agree with both. My one suggestion for reconciliation: when you can't make up your mind for a particular action, consider another factor to try to tip the scales. And if you still can't make up your mind, consider another... when you exhaust all EV-minded decision criteria and you're STILL exactly on the fence, take the lower-variance route (then go back later and figure out another relevant EV-minded factor). Now you're not intentionally sacrificing any EV, but you're reducing your bankroll requirements.

Of course, whatever benefit you derive from this strategy better be labelled "epsilon."

2ndGoat

[ACW]

I wonder if the root of this discussion is the splitting of hairs between the arithmetic and geometric means?

EV is the weighted arithmetic mean of the possible outcomes. In BJ, you can keep each bet as a fixed percentage of bankroll, and in such a case it is the geometric mean that matters. It's not hard to construct scenarios where the arithmetic mean is positive, but the geometric mean is less than one.

In poker, if you are playing within your bankroll, and changing stakes rarely (compared with the number of hands you play), the arithmetic mean is what matters. The less well bankrolled you are, the bigger the relative importance of the geometric mean, but unless you take your entire bankroll to a big bet table, your results will always more closely follow the arithmetic mean than the geometric mean.

[Toffler]

Janacek's work involved more than Kelly. You can find his paper, I think it's titled "The Theory of Optimal Betting Spreads", on the internet.

Toffler

[Cheeseweasel]

"The Theory of Optimal Betting Spreads" was written by Brett Harris.

[BradL]

Fantastic post.

-Brad

[SinCityGuy]

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I'm not familiar with the numbers, but I can basically guarantee you that the effect on bankroll growth of splitting versus not splitting tens versus a six at a +6 or +7 count (or whatever the index is) is negligible.

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Actually, it's probably negative EV when you factor in the probability of getting "the tap on the shoulder" and getting 86'ed after you split your tens vs. the dealer's six on a high count. [img]/images/graemlins/wink.gif[/img]