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_magazine/archives/?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.

[bonanz]

your example really makes no sense.

you said initially your variance will decrease over time by multitabling.

your variance will stay the same if you are using # of hands as your guideline. if i play 1000 hands in one hour or take a week to play 1000 hands my variance will remain the same.

if you are using amount of time as your guideline your variance will increase per unit of time since you are squeezing in way more hands per unit of time. so if I play 1000 hands in an hour then play 1000 hands over the course of a week, my hourly variance would be higher during my one hour session.

[axioma]

"so if I play 1000 hands in an hour then play 1000 hands over the course of a week, my hourly variance would be higher during my one hour session."

Well no [censored]. Of course, that comment is completly irrelevant.

The fact remains: if you play 200 hands in an hour the variance in your EV is less for that hours play than if you instead only played 50 hands in that hour.

I thought this was basic stuff...

[bonanz]

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


[/ QUOTE ]
me:

[ QUOTE ]
" if I play 1000 hands in an hour then play 1000 hands over the course of a week, my hourly variance would be higher during my one hour session."


[/ QUOTE ]

you:
[ QUOTE ]
Well no [censored]. The fact remains: if you play 200 hands in an hour the variance in your EV is less for that hours play than if you instead only played 50 hands in that hour.


[/ QUOTE ]

am i going crazy? your statement is the exact opposite of mine yet you still maintain that both are correct? I mean seriously someone correct me if i'm wrong in this point alone.


[ QUOTE ]
I thought this was basic stuff...

[/ QUOTE ]

[axioma]

Perhaps i should have extended that first quote you used of mine to read: "obviously, the more hands you play in a given time unit, the lower your variance (in EV for the time unit) will be for that time unit than if you played fewer hands for the same period of time."

I (wrongly) thought that people here would pick up what I was saying with little difficulty.

The next quote of yours is completely besides the point so I wont comment.

I re-state by orignal point in your third quote of mine trying to be as clear as possible.

Your point is not the opposite of mine, in the same way that 'I like cheese' is not the opposite of 'I hate arguing with people on the internet'.

anyway Ill leave this alone now. /images/graemlins/tongue.gif

[bonanz]

to quote GOT "you're wrong. I'm right. Not close"
however you are correct about arguing over the net.

link (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=1128653&page=&view=&s b=5&o=&vc=1)

[axioma]

After reading that thread im sure now we are arguing different points. Its the only possible reason for the lack of comprehension between us, unless of course one of us is mentally unstable, and the Dr. says im O.K.

One final comment and then im going to bed.

The whole 'time' issue might be whats confusing you. I only mentioned it because its clear that when multi-tabling you play more hands in an hour than at a single table.

Its the number of hands thats important here.

again, say you average 3BB/100 over 1M hands. if you somehow manage to play 1M hands in an hour (of course assuming constant skill level) your BB/100 for that session will be very close to 3 right? Closer to 3 than it would be if you only played 50 hands.

Please at least agree with that /images/graemlins/confused.gif.

Now I really am going to bed.

[bonanz]

this is the last i will post.

you are misunderstanding variance. if you play 1 million hands in one hour your variance will be higher than if you played 50 hands in one hour.

if you multitable, or play 1 million hands in one hour your winrate will approach your true winrate much more quickly. that is not decreasing variance.

take some time to think about it

[mmbt0ne]

I would jump in, but I think I explained it fine the first time, and bonanz did an great job of trying to get it through. You can't add variances (whether in terms of BB/100 or BB/hr) and come up with a variance less than any of the originals. It is statistically impossible. And there's a lot of crazy stuff you can do with statistics, so that's saying something.

[wdbaker]

you will just get where you are going faster, if you are a +EV player you will tend to have more winning sessions, if -EV player you will tend to have more losing sessions. It's still the same variance, just happens over a shorter time span.

Example with one table 30 hrs +EV player 1/2 limit = $60
Example with 3 tables 10 hrs +EV: tbl1 -$30, tbl2 $70, tbl3 -10 = $60 same as above only faster

One Street at a Time
wdbaker Denver, Co

[gaming_mouse]

[ QUOTE ]
if you multitable, or play 1 million hands in one hour your winrate will approach your true winrate much more quickly. that is not decreasing variance.

[/ QUOTE ]

Correct. It sounds like he is confusing variance with standard error, which does go down.

gm