please comment on my methods

[A_PLUS]

This is from a post I made on the MTT forum. The question was regarding the odds of TT being the best hand with a flop of JJ6.

The two scenarios were you are heads up in the small blind, vs. you are 5 handed in the C.O. and it is checked to the button, who bets.

Here is my post....

Ok, I did some calculations. The important factor we have been ignoring is the frequency that the last to act player will bet when he does not have at least one Jack.

Lets assume that your check raise will cause any hand that is does not have a Jack to fold. Simplifying things greatly.

So heads up:
opponents possible hands: 1081 [C(47,2)]
Hands with at least one J: 91 [C(47,2)-C(45,2)]
Hands bet without a J: X=(1081-91)*raise w/o J frequency
***I will assume 50% raise w/o J for now
Hands bet without a J: 495=(1081-91)*.5
Total hands bet= 586=495+91
Odds player has a Jack: 15.5% = 91/586

Now if you take into account that 6 non-jacks have been folded.
opponents possible hands: 820(41,2]
Hands with at least one J: 79 [C(41,2)-C(39,2)]
Hands bet without a J: 370.5=(820-79)*.5
Total hands bet= 449.5=370.5+79
Odds player has a Jack: 17.6% = 79/449.5


The fact that 3 players have folded doesn't change the odds to the point where the value of a raise vs. fold would change much. BUT...I think the probability that a player will bet without a Jack is significantly higher heads up than it is 5 handed. Most good players will fear a check raise (with good reason) more with 4 opponents than a solo opponent.

Personally, I would put my %'s as
80% heads up
10% 5 handed

That would change the % of time the player does have a jack to:
Heads up: apx 10%
5-way: apx 51%

The single most important factor in the hand, is the number of players, but not for the reasons suggested. It matters b/c players will bluff into a solo opponent with a much greater frequency than they will into 4 players.

thoughts?