[jaminbird]

[ QUOTE ]
If one player has seen a red card the other is less likely to see a red one as well. So on average they will bet oposite colors more often. This would mean that their edge decreases.

[/ QUOTE ]
FYP

Although their advantage does decrease (to zero) when they bet "opposite," their advantage increases proportionally when they bet "same."



The numbers work out as follows:

The odds of winning when playing alone are 26/51 which yields an expectation of
.0196 or 1/51 (((26/51)*2)-1).

When playing together they will bet "opposite" 26 out of 51 times. When they bet "opposite" they each have a 25 out of 50 chance of winning. Therefore, they have an expectation of 0 (((25/50)*2)-1) on the "opposite" bets.

When playing together they will bet "same" 25 out of 51 times. When they bet "same" then they have a 26 out of 50 chance of winning. Therefore, they each have an expectation of .04 (((26/50)*2)-1) on "same" bets.

Therefore, when playing together each has the same expectation as the other.

Their expectation when playing together is the same as when playing alone because: They have a 26 in 51 chance of an expectation of 0 and a 25 in 51 chance of an expectation of .04. (26/51*0)+(25/51*.04) = .0196 or 1/51