I need help with calculating odds.

[soxfan70]

I'm playing in a No Limit cash game the other day with pocket 10's, one opponent and a board of K /images/graemlins/spade.gif K /images/graemlins/diamond.gif 2 /images/graemlins/club.gif, rainbow. He checks, I check (maybe should have bet there, but for this discussion, that mistake is irrelavant.) Turn brings the 4 /images/graemlins/diamond.gif and a pot sized bet from my opponent. Thniking that he wouldn't bet with a K, but would rather check and hope to trap, I raise 2X the pot, figuring he'll lay it down here. to my surprise he calls, and the river brings the 8 /images/graemlins/diamond.gif, and a bet from him for the rest of my stack, which I call and am totally flabergasted when he shows 6 /images/graemlins/diamond.gif7 /images/graemlins/diamond.gif for the flush! I express my dissatisfaction with his turn call, and he proceeds to tell me that he was only a 3-1 dog, and was getting more than that to call and chase the flush. Now for my questions:

1) Was he mathematically correct to call and chase?
2) If so, how did he arrive at his being a 3-1 dog?
3) Does the pair of K's change the odds due to the fact that there is a potential for a full house?
4) What publications can I read to help me in calculating odds in that fashion, because there is NO WAY I make that call if I'm him.

Please help!!!

[Ghazban]

If the pot is X, he bets X (so now 2X in the pot), you raise to 2X (so now 3X in the pot) and he is getting 3:1 on that call. If he assumes his 9 diamond outs are all good (which they aren't as the 10 will give you a full house), then he has a 37:9 chance (~4:1) of hitting his flush on the river. If nobody will put any more money into the pot, he would be wrong to call here. However, if his flush hits, he is assuming he can get your whole stack (which he did) so, factoring in the implied odds, he'll get much more than 4:1 when his flush does hit so he calls.

I suspect the pot sized bet on the turn was not one he wanted you to call. He would've preferred to win it right there. However, by raising the minimum, you don't give him poor enough odds to stop chasing.

[Precision1C]

Some added information would be necessary to come to a complete answer to your questions. How much money could be bet on the river? Were you always going to call the all in bet at the river if a diamond hit? This information radically affects implied odds.

1. Assume that there was $100 in the pot at the flop, $100 bet on the turn by your opponent and you raised it $400 more so that at the point your opponent needed to call a $400 dollar bet with $700 dollars in the pot. With a 9 outer your opponent was getting 9:37 or 4.1 for 1 odds with the pot odds offering 1.75 for 1. If you never intend on calling if a non ten diamond hits on the river you opponent has made a large error calling and you will bust him if a DT comes on the river. However if you always intend on calling the all in bet on the river your opponent has made a reasonable call if $950+ can be bet on the river. However the fact that a DT bust your opponents changes these odds calculations but he didn't have that information when he called the bet on the turn.

2. Assuming that any diamond wins for him and all non-diamonds lose he had 9 winning cards and 37 losing cards on the river giving him a 4.1 for 1 dog.

3. The KK in dummy changes the calculations. Now the DT gives you a full house and busts your opponent since you have a full house so your opponent only has a 8 outer not a 9.

4. Sklansky's advanced book on hold'em has a section on pot odds and implied odds and how to calculate them. However there are really huge swings in implied odds in hold'em since the last card is a known quantity. If your opponent has put you on the correct draw instead of getting implied odds you end of giving implied odds since your opponent will only call your river bet when he is winning and fold if he can't beat your flush making calling on the turn tough. That is why you semi-bluff on the flop and turn in Hold'em so that when the river comes you can't be put on a flush with any certainty.

Hope this helps -Precision1C