Help me understand these probabilities.

[sunek]

Hi

Last night I was playing a game with some new and very loose and aggressive players. When we were four players left the following hand occurred. I folded and the three others went all in on each other and they had about the same amount of chips.

Their respective hands were A[img]/images/graemlins/club.gif[/img] 6[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/diamond.gif[/img] T[img]/images/graemlins/diamond.gif[/img], 6[img]/images/graemlins/spade.gif[/img] 5[img]/images/graemlins/spade.gif[/img]

I my opinion the guy with 6[img]/images/graemlins/spade.gif[/img]5[img]/images/graemlins/spade.gif[/img] was super lucky since he won the hand, so I used poker stove to calculate the probabilities that each of the hands against each other. I actually thought that the A6 would be favorite and that 6[img]/images/graemlins/spade.gif[/img]5[img]/images/graemlins/spade.gif[/img] was a huge underdog but is does not seem to be like that.

Hand 1: 33.5150 % [ 00.32 00.01 ] { Ah6c }
Hand 2: 41.1803 % [ 00.41 00.00 ] { KdTd }
Hand 3: 25.3047 % [ 00.24 00.01 ] { 6s5s }

Why is K[img]/images/graemlins/diamond.gif[/img]T[img]/images/graemlins/diamond.gif[/img] the favourite to win this hand and why does it not hurt 6[img]/images/graemlins/spade.gif[/img]5[img]/images/graemlins/spade.gif[/img] very much that there is a 6 with a better kicker on one of the other hands.

Thank you

Regards

sunek

[Artsemis]

The A6 is the only non-suited cards, and its not connected in any way which will give the others a slightly higher bit of percentage. Also, like you pointed out, sharing the 6 hurts both of the other two hands.

[AaronBrown]

Let's do some rough figuring. Call it 8% to make a flush with two suited cards and 2% for every possible straight. A[img]/images/graemlins/club.gif[/img] 6[img]/images/graemlins/heart.gif[/img] gets nothing, K[img]/images/graemlins/diamond.gif[/img] 10[img]/images/graemlins/diamond.gif[/img] gets 12% (flush plus two straights), 6[img]/images/graemlins/spade.gif[/img] 5[img]/images/graemlins/spade.gif[/img] gets 16% (flush plus four straights).

The remaining 72% is divided up 34% for A[img]/images/graemlins/club.gif[/img] 6[img]/images/graemlins/heart.gif[/img], 29% for K[img]/images/graemlins/diamond.gif[/img] 10[img]/images/graemlins/diamond.gif[/img] and 9% for 6[img]/images/graemlins/spade.gif[/img] 5[img]/images/graemlins/spade.gif[/img]. That seems about right. The first hand wins if nobody pairs, and he has the high card to pair. The next hand has the second and third highest pairs, and no shared cards. The last hand needs a five to win without a straight or flush.

[sunek]

Thanks to both of you.

sunek