Ribbit's Edits

[Aisthesis]

Is this just basic statistics? Very nice equation, and I agree about putting it somewhere permanent.

We could also look at it like this:

(BR*2*WR)/SD^2 = -ln(ROR)

Well, was hoping to explicitly formulate ROR, but I like leaving ln more than putting in the e function...

[Silent A]

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really? I remember this came up before and you told me increasing your SD does not massively increase your bankroll requirement (unlike decreasing your winrate). My SD is something like 70ptBB/100 and I don't think this is particularly high-variance, but I would be happy with 60BI for any game I thought I had a noticeable edge in.

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I should also say that there is an issue of uncertainty. Your PTO SD numbers should be very close to your "true long run" deviation.

Win rate, however, is very difficult to estimate. If you play at levels where 3 ptBB/100 is very good, it takes a lot of hands to estimate your win rate within 1 ptBB. And by the time you have this many hands, your old data may no longer be valid. If your estimated win rate is 3, a difference of +/- 1 in your win rate would make the difference between needing 30 or 60 buyins.

[Troll_Inc]

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So the question for me is, does the SD calculated for every hand accurately model the SD of the big pots?

It should be fairly obvious that the SD in poker is highly dependent on the frequency and size of large pot events. As such, I think it's a reasonable parameter to use. Furthermore, it's fairly well established that SD is relatively easy to estimate.


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Focusing on the big pots is good, but you are looking at the wrong metric (and using the wrong type of statistics).

Let's look at two players. Both have the same number of "big" pots and all are of equal size. However, Player A has 65% of his big pots positive while Player B has just 35% of his big pots positive. Both will have roughly the same SD.

On another point, standard winrate analysis takes too much into account all the pots the player does not win or lose much on, i.e. most pots (99% or more).

A golden rule of statistical analysis is that you must take into account, i.e. not ignore, all variance possible. The variance associated with hands you don't play is clearly different from the variance associated with the big pot hands. It must be dealt with separately.

Going back to my highway example, I'll modify the situation. Let's make it a north-south 16 lane highway. You have a small number of cars traveling really fast going north, a small number of cars traveling south, and then you have a whole bunch of cars stopped or going really slowly. If you want to understand the net movement of cars over a whole week, but you only measure a 10 minute sample, I hypothesize that the most accurate thing is to break down the groups and analyze each separate group using more than just calculating average movement and variance (stdev). Then, and only then, can you come back and make a better guess at the population mean.

[Silent A]

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Let's look at two players. Both have the same number of "big" pots and all are of equal size. However, Player A has 65% of his big pots positive while Player B has just 35% of his big pots positive. Both will have roughly the same SD.

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I don't see how this is a problem since expected win rate is also part of the calculation. As such, Player A's ROR is much lower than Player B's.

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On another point, standard winrate analysis takes too much into account all the pots the player does not win or lose much on, i.e. most pots (99% or more).

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Not as much as you seem to think. The only real effect these have on the SD is by adding hands in the denominator. Their effect is on the frequency of big pots. I admit that the SD does not obviously balance these two effects particularly well. But it isn't obvious that it does a terrible job either.

For now, here's a peek at a frequency histogram of my last 25k PLO 50 hands. I didn't run all that well and only showed about a 1.5 ptBB/100 hands (Boo).

Each column represents a range of +/- $2.5 around the value on the x-axis. BTW, since the top of the graph is cut off. The central column at $0 (-2.5 to +2.5) represents almost 22k of the 25k hands.


Someday, I'd like to do a Monte Carlo simulation with this data to test how reasonable the normal approximation is for bankroll estimation.