Variance and making deals...

[R_Ellender]

Recently, a friend and I began trading out 20% of ourselves at each tournament. Provided we have the same skill level, and our total prize money is $300 every five $20 tournaments, our expected earnings every five tournaments would be $200.

300-(0.2)(300)+(0.2)(300)-(5)(20) = +200

Over 100 tournaments, we'll both have our hot streaks and cold streaks. About 20% of the time, I place in the money, and since my friend has the same skill level, he also places in the money in 20% of the tournaments he enters. The chances of either one of us finishing out the money is obviously 80%. However, the chances of us both placing out of the money is 64%.

(0.8)(0.8)=0.64

And then the chances of us both not finishing in the money in two consecutive tournaments is about 41%.

(0.64)(0.64) = 40.96%

However, playing by myself in these tournaments(no deals), the chances of me placing out of the money in two consecutive tournaments would be 64%... 80%*80%.

Since we expect to earn the same amount of money over time, does deal-making cut down on our variance? If we never traded out 20%, we would still both make 200 over five tournaments. However, he could go five tournaments without placing, and I could get lucky and place in three out of five. While he is only getting a small percentage of his total expected profits in that scenario, his poor results are compensated for by my great results. I know our downswings would be inevitable, but would they be less frequent and severe?

Yes

[Wacken]

It does the same as playing 20% more games with 20% lower stakes. So yes, that lowers your variance.

As another responder said, the answer to I think all of your questions is yes. Whether you are sharing 20% of yourselves, or 5% pr 100%, the concept is the same.

You are more or less working to a common bank. There have been many detailed analyses on these situations long before the poker boom. They mostly came about from early card counting work and team play in blackjack. Some of Uston's and Griffin's work covers the general concepts in detail.

In short, by working from a common bank, you should be able to reduce variance, because you are able to reduce standard deviation. Together you are able to reduce the likelihood of swings that you may be more likely to incur singlely.

More importantly you should be able to reduce risk of ruin. This is not to say that you couldn't both simultaneously run into a bad swing, and see a worse negative fluctuation than a single player may see. It is just less likely. It also assumes that you are both winning players. If one or both of you are losing players, then the end game is the same, it just may take you longer to get there.

It makes a lot of sense logically, but the mathematics backs up all the way. But this is not without risk in and of itself. The players have to be able to trust each other implicitly and or explicitly. They have to be sure they are working under common sets of rules, etc. This is not easy to do all the time.