Variance in 4 tables?

[BK1248]

I have always read on here that 300 bb/100 is usually one of the top swings that a winning player might face, but my friend disagrees with this statement.

He has been playing live for a living for 15 years or so and says that the swings on 4 table should be no more than the 1 table. I think he is incorrect because I have never had more than 100 bb per hour loss in a casino but i have had 300 bb/100 downswings 2-3 times over the last 4 years.

Does anyone have an explanation to who is correct?

ty

[TomCollins]

You both are.

You have more variance/hr, but the same variance/100 hands.

[jjacky]

your variance per 100 hands is the same. the variance is 4 times higher with 4 tables (that means the SD doubles). and the EV is 4 times higher as well of course.

i would agree with your friend. you don`t need a biger bankroll for 4 tables. here is why: a 300 BB bankroll is designed to have a very low risk to go broke if you play for ever and add a small percentage of your winnings to the bankroll. if you play 4 tables everything is the same but it's faster. if you wont go broke in eternity, you wont go broke in eternity/4.

[BK1248]

.

[AaronBrown]

There are a couple of reasons that this question is hard to answer. One is that you might change your strategy if you lose a lot. An obvious example is you might only have 300 BB, so that's your maximum loss in any number of tables.

But if we assume you keep playing poker, ignoring all gains or losses, then it's a pretty good assumption that your expected win rate and standard deviation are constant. You are not guaranteed to never lose more than 300 BB, but it's a very event.

Suppose, for example, that your expected win rate was 10 BB per hour and your standard deviation was 133 BB. To lose 300 BB in one hour would be 310/133 = 2.33 standard deviations below the mean. Losing that amount or more should happen only 1% of the time.

Over four hours, you have an expected gain of 40 BB, so a 300 BB loss is 340 below expectation. The standard deviation doubles to 266, so you'll lose 300 BB or more about 10% of the time instead of 1%. Your 1% loss point is about 580 BB.

Eventually, however, the expected value begins to dominate. Over very long periods of time the chance of a 300 BB loss declines (although the probability that you have experienced a 300 BB loss at some point continues to go up).

So, on one hand, it's incorrect to state the maximum likely loss per hour. It goes up more slowly than that, both because positive expectation makes more difference over longer intervals, and because the standard deviation only goes up with the square root of the number of hands or hours played. But it's also not right to say the one table maximum likely loss is equal to the four table value, unless your expected return is unrealistically high compared to your standard deviation.

[jjacky]

very good post, but it might lead to wrong conclusions. your calculations were based on a SD of 133 BB per hour while the real SD should be between 32 and 40 BB per hour for 4 tables. that leads to a dramatically reduced probability to go broke with a bankroll of 300 BB.

one more point came in my mind that i didn't mention in my first post. if you have a probability p(n) to go bust in n hours and a probability q(m) to go broke in m hours of play at 4 tables at the same time, the following is true:
p(n) = q(m) if 4*n = m
or
p(4n) = q(m)