Quick question about SD

[SA125]

I'm looking for some layman's help here for an easy way to understand how to relate your SD to your results so I can look at my PT SD numbers and relate them to my hands played and results. For example, can the SD number be applied to every 100 hands played and go in one direction for a long time?

Let's say your SD is 15 BB's per 100 hands/ 15 BB per hour. You have played 5K hands. How does your SD figure into the total hands played to show the range of winning/losing? Do you have to use your present results (winner/loser) in that calc to get it? Does it change if the hands played is 100K?

Any help would be greatly appreciated. I've read Malmuth's Gambling Theory but not so swift with advanced calc's. I can't get an easy take on applying it. Thanks.

[AaronBrown]

Standard deviation of total profit or loss goes up with the square root of the number of hands or amount of time playing. So if it's 15 big bets per 100 hands, it's 30 big bets per 400 hands (the square root of 4 is 2), 45 big bets per 900 hands, and so on. This is a theoretical result based on each hand being independent. If you go on tilts, move to a different limit structure or otherwise change your play over the interval, the result will not be valid.

One way to think of standard deviation is to note that if you flip a fair coin for $100, the standard deviation of the bet is $100. So if you play 10,000 hands of poker, your standard deviation is 150 big bets, so your gamble has the same risk as flipping a coin for 150 big bets. Hopefully you have an expected value over 10,000 hands that is something near or above 150 big bets; if so you can be a consistent winner. If not, you're gambling.

Standard deviation is much easier to measure than expected value, it also tends to be more constant as long as you stay in the same type of game and don't change your play (or if you adjust for strategy and limit structure). Therefore, for practical purposes, it can be computed regardless of your expected value and tends to remain pretty constant even if your expected value goes up and down.

[SA125]

That's a great answer. Thanks. I think I got it. I remember the way Sklansky used SD with regards to an estimate of hourly win rate.

But for just SD, is this right then - for 100K hands and 15BB SD, you're SD is 1500BB. 10K being square root of 100K and 100 x 15 being per 100 hands of 10K?

[AaronBrown]

In your example, you had an SD of 15 BB per 100 hands. 100,000 hands is 1,000 times that, so the SD goes up by the square root of 1,000 or 31.6. That gives you an SD of 474 BB over the period.

It's true that 10 is the square root of 100, but 10K is not the square root of 100K. You have to take the square root of the K as well, it's 31.6. So the square root of 100K is 316 (the square root of 100, 10, times the square root of K, 31.6).

[SA125]

Thanks again. FWIW, I went to a Catholic grammar school and was light years ahead of most of the other kids when I started in my local public HS. By my junior year, I was a stepford moron like the rest. Begged my algebra teacher to pass me because I got a 90 on the mid term and a 45 on the final. Too many concerts I guess.