Does Multi-tabling increase variance?

[jokerthief]

I was trying think this problem through logically today and my opinion is leaning toward no, but I have had no formal training in statistics so I am not sure if my logic is worth anything. Could some of you math geniuses please give me some insight into this? The reason I am asking is because I am trying to decide if I need more than 300 BB in my bankroll because I play 4 tables at a time. Thanks for any input.

[Nottom]

Yes, your variance does go up, but not nearly as fast as your winrate should go up. In theory if you could play as well at 4 tables as one your winrate would be 4 times as high and your Std Dev would be twice as much.

As a result, you can multitable with basically the same bankroll you can single table with. There are about a million threads that do the math for you here but it basically all amounts the the fact that playing 4-tables is effectively the same as playing 4 times as long and is not the same as playing at a limit 4 times as high.

[aces961]

This really depends on how you define your win rate and varience. If you do so in terms of Big Blinds per 100 hands, then when you play 4 tables if your win rate stays the same then your varience will stay the same. Now if you define it as big blinds per hr then assuming 4 tables corresponded to a increase by a factor of 4 in win rate, your standard deviation would go up by a factor of two.

The risk of losing your bankroll after a certain number of hands would be the same in either of these cases assuming your win rate per 100 hands per table stayed the same no matter how many tables you play.

Now in reality there will probably be a decrease in win rate per hand as you go to more tables so your risk of going broke in x hands will be higher if it was done at multiple tables than at one table.

[phisfliuch]

I think Howard Lederer addressed this on rpg. Try a googe groups search and you should find it.

[zerosum]

Dan Kimberg recently addressed this point in an article titled "Reducing Variance With Simultaneous Play."

The title suggests his opinion. Here's a link to the article.

http://www.cardplayer.com/poker_maga...es/?a_id=14233

[mmbt0ne]

That article says you can reduce your variance by playing 3 5/10 tables instead of 1 15/30 table, not that multiple tables of the same limit will have a smaller variance. Unfortunately, there is no way to add multiple tables, which each have variance X we'll say, and end up with an overall variance less than X.

The most important point, though, is what Nottom pointed out. Your win rate should increase enough to take the some of the sting of an increased variance.

[axioma]

anyway you look at it, multi-tabling reduces variance over TIME.

obviously, the more hands you play in a given time unit, the lower your variance will be.

[pzhon]

[ QUOTE ]
anyway you look at it, multi-tabling reduces variance over TIME.

obviously, the more hands you play in a given time unit, the lower your variance will be.

[/ QUOTE ]
No, that's not obvious. It's wrong by the usual definitions. You must be using a nonstandard definition of variance.

If you bet $1 on a fair coin-toss, the variance is 1. If you bet $1 each on 10 independent coin-tosses, the variance is 10. If you bet a total of $1, evenly spread out on 10 independent coin-tosses, the variance is 0.1. The standard deviation is the square root of the variance, and it tells you the scale of typical results. Sqrt(10)~3, so after betting $1 10 times, typical results would be to win or lose about $3. The swings are much greater than if you only bet once.

To reduce your variance per hour while multitabling, you need to play at lower limits.

[bonanz]

[ QUOTE ]
multi-tabling reduces variance over TIME.

obviously, the more hands you play in a given time unit, the lower your variance will be.

[/ QUOTE ]

wow, very wrong

[axioma]

right.

lets say you have made 3BB/100 over the last 1,000,000 hands you have played.

you play an hours session, of lets say 50 hands per table per hour.

in situation A you play at one table (50 hands). In situation B you play 4 tables (200 hands). Lets say your profit in situation A is Ap, and for B, Bp.

Are you REALLY claiming that |Ap - 3| < |Bp - 3| ?

Interesting.