Odds against two random hands

[glfrjack]

Situation

Home game, 7 people, I'm in the big blind with JT. Player to my left goes all in in-the-dark. Everyone folds to the small blind who also goes all in in-the-dark. Pot's giving me 2-1 on my call.

Question: What are my chances (odds) pre-flop to win against two random hands?

I ran it through some simulation software (Poker Stove (http://www.pokerstove.com)), and got the following numbers:

Monte Carlo:

60,641,369 games 121.422 secs 499,426 games/sec

.......... equity (%) win (%) tie (%)
Hand 1: 39.7542 % 38.46% 01.29% { JTs, JTo }
Hand 2: 30.1189 % 28.84% 01.28% { random }
Hand 3: 30.1270 % 28.85% 01.28% { random }


Brute force:

114,271,536,456 games 269.469 secs 424,061,901 games/sec

.......... equity (%) win (%) tie (%)
Hand 1: 42.1175 % 41.27% 00.85% { JTs, JTo }
Hand 2: 28.1654 % 27.34% 00.83% { random }
Hand 3: 29.7171 % 28.28% 01.43% { random }

So about 40/30/30.

It was nowhere near completed, but the numbers seem reasonable.

In case you're interested, here's an analysis of JT against other hands:

2:1 fav over lower unpaired cards (98...32)---33.8% of hands
3:1 fav over dominated hands (J9...J2 and T9...T2)----19.3% of hands
1:1.2 dog against low pairs (99...22)---3.6% of hands
1:1.2 dog against over/under (i.e. A8, K4)---29% of hands
1:3 dog against dominating hands (e.g. AJ, KT)---7.2% of hands
1:2 dog against overcards (KQ+)---3.6% of hands
1:4 dog against overpairs---1.8%


The important facts are:

-You're a big dog against maybe 13% of all hands
-You're a big fav over approx 54%,
-The rest (33%) you're close to even money but slightly behind.

P.S. Thanks for the question, I've been wanting to go through this math for a while for push/fold decisions late in tournaments, but it's awfully boring.