Figuring out favorites

How do you calculate who has the better hand after the flop? For example, player A has 44, player be has KQ of spades and the flop is Js10h4s. Please show your work so I can learn how to do it myself. Thanks.

I'll take a stab...


KQs has an open end straight draw as well as a flush draw. He has the following cards to help him:

4 Aces, 4 Nines

6 Spades (13 - 4 = 9 - Ace - Nine - Ten = 6)

Total of 14 cards that KQs can win with.

There are 45 unseen cards, so he has a 14/45 chance to get what he needs on the turn.

If he does hit on the turn then there are 10 cards (3 Jacks, 3 Tens, 1 four, and 3 of whatever card hit the turn) that can kill him on the river.

There will be 44 cards left so thee is a 34/44 chance he will see a safe river card.

If he misses the turn, he has to miss it safely. There are 24 safe turn cards (24/45) and then he has (14/44) chance of hitting his card on the river.

So he has a (14/45)*(34/44) + (24/45)*(14/44) chance of winning. This is a 41% of winning.


So 44 will win 59% of the time and KQs will win 41% of the time.


44 is the better hand.


I hope I got that right....

***********

Hi Chuck,

Also check out the thread where I asked about this same problem.


Beginner ?, hand vs hand odds


It is explained very well there.

GL,

Allan

So the way to go with this is to pick one of the hands and look at all the possible ways it can win. The KQs hand has two scenarios to win: (1)hit on the turn and not get beat on the river and (2)miss the turn and hit the river. Add both of those odds together and determine the favorite.


The example was a hand I saw a while ago in a NL game. The KQs acted first (heads up) on the flop and made a massive all in bet, the 44 player, who had a mountain of chips himself, showed his hand and mucked.


Thanks.

Didn't see that Allan. Thanks for pointing that out. Think I'll try to solve it and then check to see that I got it right.

4h4d KsQs

% chance of outright win 59.696970 40.303030

% chance of win or split 59.696970 40.303030

expected return, % of pot 59.696970 40.303030

fair pot odds:1 0.675127 1.481203


You were pretty close ;]


Chris