Help with how to calculate results

[teemu_69]

Recently I was all in with Qd6d on a 6c3d4d board against AcAs... I thought I had a pretty good shot but when we dealt it out I lost the hand. I went to twodimes.net to see how bad I was losing after the flop (which is where I went all in) and the results surprised me:

pokenum -h ac as - qd 6d -- 6c 4d 3d
Holdem Hi: 990 enumerated boards containing 6c 4d 3d
cards win %win lose %lose tie %tie EV
As Ac 479 48.38 493 49.80 18 1.82 0.493
Qd 6d 493 49.80 479 48.38 18 1.82 0.507

I thought about it for a while and even tried to calculate how I could be favored to win the hand and I couldn't figure out how to set it up or what outs I would have besides Q,6,D... If someone could please show me how to calculate the chances of me winning this hand and explain how I was a favorite at this point I would really appreciate it. Thanks!

[dabluebery]

The two dimes sounds right.

If a queen falls, a six falls, or a diamond falls, you win. 3 queens left, 2 sixes, and 9 diamonds makes 14 outs as far as I can tell.

That's a lot of outs. Over 50% that you hit one, subtracted by the cards that can fall so you both make a straight, subtracting the chances he hits a boat or a wheel straight.

[Bozeman]

You have 14 outs twice, so you will hit 1-31/45*30/44=53% of the time. However, you will occasionally hit and still lose: if you hit a Q he has 8 outs for better 2 pair, if you hit a 6 he has 2 outs, and if you hit Ad he has 9 outs.

[teemu_69]

Thanks for clearing that up for me Bozeman. After I posted and dabluebery responded I figured out how to get close to the percentage that you did, but couldn't get it quite right until reading your post.

[Bozeman]

Just wanted to check that I could count all the possibilities:

990 combinations total, you win
36 dd
8*36=288 dx (not Ad)
1*27=27 Adx (x!=6 or 3 or 4 or A or d)=351 flush or str8 fl

1 66 quad

6 6q
6 63
6 64
3 qq=21 fullhouse

2*24=48 6x (x=2,5,7,8,9,t,j,k not d) trips
3*24=72 qx (x=2,5,7,8,9,t,j,k not d) 2 pair


3*3*2=18 draws=str8 on board (52 or 57, no d)

win 493/990=49.8%

win + 1/2draw= 502/990=50.7%

harder than believing 2dimes or other computer,
Craig