Full ring versus 6 max

[Mark1808]

Full ring (9 or more) plays a lot tighter than 6 max. I mentioned to a good player that once the first 3 fold in a 9 handed game the game essentially becomes 6 max. He says that 9 handed is tighter due to the greater chance that at least one other player has a big hand. I contend that once the first 3 have folded the likelihood of the remaining 6 having a good hand is the same as a 6 max game, he contends the fact that 3 already have folded make it more likely that one of the next 6 have a good hand.

It seems to me the 6 cards folded by the first 3 players does not materially affect the likelyhood of a good hand among the 6 remaining.

Any comments as to who is right?

[AaronBrown]

I think you're basically right, but it comes down to the definition of "materially."

Suppose that people play any hand with two cards Jack or better, 20% of hands with one card Jack or better and 5% of hands with no cards Jack or better. Overall, that's 20.1% of hands.

The average hand has 0.62 cards Jack or higher, the average hand played has 1.33 of those cards, the average folded hand has 0.44. So each folded hand slightly increases the number of cards Jack or higher you expect in the rest of the deck, and therefore increases the probability that the remaining hands will be played.

After three folds, the chance that a hand is playable goes from 20.1% to 21.4%. Material? That's up to you.

Of course, this is oversimplified, but I think it captures the size of the effect.