Dear Wizard: Multiple Tables Decrease Variability??

Dear Wizard,

I have read several articles now on how 'theoretically' playing multiple tables in online poker decreases variability??

I'm not sure I agree, If a player is playing the same strategy on each table, then we could say each table is an IID RV. and the overall variance becomes the sum of the independent variances for each RV. Which increases variability, but also increases expected value.

I would even argue that different strategies would give the same effect.

What are your thoughts?

koooee

It would depend on how the statement is phrased. It would lower volatility to play 3 tables with an average bet of $10, compared to one table with an average bet of $30, for an equal amount of time. However, obviously, three games of $10 would have a greater volatility than one game of $10. Same principle applies to any game.

I'm not sure I'm following.

If I play 4 tables of the x/x NL(or x/x limit) as opposed to 1 table of x/x NL(or limit) isn't the only real change the number of hands I play?

I'd simply be playing more hands and as the sample gets larger I should approach my actual winrate.

Each hand is in and of itself an IID RV. and since each event is independent from the next, the more 'variables' you add will increase the variability.

When you say winrate, do you mean the percentage of hands won? or the Expected Value per hand?

Winrate is expected value per hand. For most poker games this is generally expressed as XBB/100(the number of "big bets" per every 100 hands).

I'm not a huge student of statistics, so I'm not entirely sure what variability,variance,etc all mean to those who have actually studied statistics.

Poker players tend to have their own meanings for these words and we work under the assumption that "variance" decreases given a larger sample size(central limit theorem).

More tables= more hands.

In order to answer your question, you need to be more exact in the framing of the question. For example-you speak of an independent identically distributed random variable, but you do not state what it is. Is the RV the amount of chips you have at a single table or the total amount of chips you have at all tables being played? Do you have a bankroll for each table or bankroll spread over all tables. Are you betting the same at each table? Do you vary or flat bet? You have to be more exact if you want a mathematical answer.

That being said, there are interesting problems to analyse here. If you were playing a game of chance such as flipping a coin or craps and could assume that the tables are independent, then the variance of the sum of the random variables is equal to the sum of the variances, assuming we have agreed on basics of the variable itself. However, I am not sure that I can assume an IID RV in a poker game. Because of poker is not entirely a game of chance but has some skill involved, at least that is what I have heard. Since you are playing with your own set of skills, I am not convinced that the RV's are independently distributed because your personal style of play would highly correlate the RV's. Further, since you are playing a different set of opponents with different skills at each table, I cannot convince myself that the RV's are identically distributed. Therefore, I cannot say that the variance of the sum is the sum of the variances. It may be the case that the variance of the sum is the sum of the covariances, but I haven't thought that aspect through yet.

Therefore, since you stated " . . . the overall variance becomes the sum of the independent variances for each RV." as the crux of your argument and this statement is false, I cannot accept your conclusion as valid, that variability increases. It may be correct, but you have not shown that it is so.

Clearly all of you are more well versed in statistics than I am. For that reason I don't doubt that your answers are technically incorrect. However, I don't feel those answers address the actual question at hand.

If I understand correctly you are speaking of the difference between actual winnings and expected winnings.

The law of large numbers dictates this will become larger as our sample grows.
Overall winnings are not that meaningful here.

As I alluded to above what we care about is our winrate. Winrates are more related to expected value and therefore converge on their true value over an infinite sample.


For cash games the most used way to express a winrate is X Big Bets/100 hands.
For example, in a $1/$2 NLHE game a 5BB/100 winrate would mean the player wins $20 for every 100 hands played(Big bets are always used regardless of whether the game is limit or not).

For tournaments ROI is typically used.