Collusion Performance for Ultimate Texas Hold’Em
I finally got around to simulating the effects of player collusion in Ultimate Texas Hold’Em. Implementing preflop collusion, and the improved 2nd nut kicker and 3rd nut kicker strategies, the house edge is reduced from 2.2% to 1.6% for 6 players. While this is a small average gain, the real benefit comes from the reduced variance gained by not raising marginal hands when copied with other players.
By checking marginal copied hands, the session outcome distribution improves as shown below. Assuming a bankroll of 200 Antes, a goal of 20 Antes, and a maximum session length of 250 hands, the improved strategy reduces the probability of busting out from .20% down to .13%. The probability of reaching your 20 Ante win is reduced from 69% to 68%, but the distribution for the in-between cases improves as shown.
Session outcome probabilities for 200 Ante bankroll, 20 Ante goal, 250 max hands.
[Note: the low-variance strategy used for the distribution does not raise any basic strategy preflop checking hands; it is designed to minimize variance, and simulates at 2.2% house edge.]
Discount Gambling 
If we as a 6 player group know the all hole cards we still don’t gain an edge over the house as a group?