Concerning variance

[Atropos]

Hey folks,
I asked this in the MTT forum too, but it seems nobody knows it. Here is the problem:

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Assume two players of equal MTT skill and play the exact same number of tournaments of the same buyin. They have an agreement to split their winnings 50%. Winnings are defined as payouts - buyin.

Here an example:
200$ Buyin, Player A busts, Player B cashes and gets 210$
--> 10$ are split 50% between them.

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How much does the variance go down for each individual player by this?

[BruceZ]

[ QUOTE ]
Hey folks,
I asked this in the MTT forum too, but it seems nobody knows it. Here is the problem:

------------------------------------------------------------
Assume two players of equal MTT skill and play the exact same number of tournaments of the same buyin. They have an agreement to split their winnings 50%. Winnings are defined as payouts - buyin.

Here an example:
200$ Buyin, Player A busts, Player B cashes and gets 210$
--> 10$ are split 50% between them.

------------------------------------------------------------

How much does the variance go down for each individual player by this?

[/ QUOTE ]

The variance for each player per tournament stays the same.* It is the same as if a single player played in twice the number of tournaments. The advantage of sharing a bankroll is that they will have a lower risk of ruin than if they each played the same tournaments separately with a smaller bankroll. They can also play for twice the stakes and make twice the money with the same risk of ruin as if they each played separately with half of the bankroll each.

*As long as they play separate tournaments, otherwise it can differ very slightly due to the correlation of their results.

[Atropos]

[ QUOTE ]

The variance for each player per tournament stays the same.* It is the same as if a single player played in twice the number of tournaments. The advantage of sharing a bankroll is that they will have a lower risk of ruin than if they each played the same tournaments separately with a smaller bankroll. They can also play for twice the stakes and make twice the money with the same risk of ruin as if they each played separately with half of the bankroll each.

*As long as they play separate tournaments, otherwise it can differ very slightly due to the correlation of their results.

[/ QUOTE ]

Hi, thx for your response, but I think it is wrong, because I was not really talking about shared bankrolls. A shared bankroll for me means both players play a 200$ tournament. If one player busts out, the other gets a payout of 210$, the overall result would be -95$ for each player.

I am however talking about a scenario where only the profits are split 50%. Here it would be:
Bustout Player: -195$
Payout Player: +5$

It seems this still has some influence on the variance/risk of ruin, but I'm not able to calculate how big it is.

[alThor]

Suppose X (or Y) is the payout for a player in a tourney. Instead of experiencing Var(X), you now experience Var(.5X + .5Y) = .25Var(X) + .25Var(Y) + .5Cov(X,Y) of risk.

Ignoring the covariance (which is slightly negative), this is half the variance of playing by yourself. Maybe it's better to think of standard deviation, which becomes sqrt(.5) of what it was before.

alThor