I was thinking about how great an advantage a player would have if they were allowed to play multiple hands simultaneously in a single game of poker. In other words, all hands get dealt normally except some set of the hands may share information and must bet from a single (albeit larger than the rest of the players') pool of money.
My initial reaction was that this is a huge advantage. Being able to know what some of the other hands are? I wish! But after I thought more about it I changed my mind. It's still undoubtedly an advantage but not as great as I first though.
Let's say you are playing 5 out of 9 hands on the game. You have a 5/9 chance of winning any given round. But you are also paying 5 times the blind and any bets. So at face value, before any information sharing, this is still a completely fair game.
When you take into account the ability to share information you will have the opportunity to fold some of your weaker hands early (ie. hands which will likely, maybe definitely, not beat some of your other hands). This is where I believe the primary, non-psychological, advantage lies. You are able to increase your reward/risk ratio this way.
So now I'm wondering how one would come to an optimal strategy for playing poker in this manner? Are we able to quantify the advantage achieved by playing like this? What other ways you can use the extra information to gain an advantage?