Pot odds v Implied odds

[DoctorWard]

You are heads up at the end of a $10+$1 single table tourney. You have $7,000 in chips and your opponent has $8,000. The blinds are $300-$600 and you are the big blind with your opponent on the button. He's first to act and raises it to twice the big blind, or $1,200. You look down at your cards and you have 6s-9s you flat call the raise to see what the flop brings. The flop comes 8c-Ks-7s you're first to act and you bet the minimum, $600. Your opponent raises to the pot-size pre-flop, $2,400. At best you put your opponent on top pair but given previous play he's probably got a pocket pair and hit a set on the flop. What do you do ~ Call, Fold, or Raise (if Raise by how much)?

[intheflatfield]

IMHO, depending of course on what kind of player he is. If I bet the min and get raised, I either fold or push. The likeliehood of him hitting trips heads up in this situation is less lilely than either TP or 2 pair.

Plus, if he did hit trips w/ p k's my guess is that he would have slow played a bit more. I put him on something like tp, good kicker.

[bobman0330]

Not a probability post.

You're a slight favorite over AK and a 41% dog against a set. push.

[DoctorWard]

I originally wrote "your opponent on top pair but given previous play he's probably got a pocket pair and hit a set on the flop", lets assume he has hit a set. For probability purposes it does not matter which set he has hit as they all have 591 combinations of winning from 45C2 possibilities, or 59.70% of winning.

In this game the pot was $1,200 + $1,200 (pre-flop) then $600 + $2,400 (to this pot), or $5,400. The pot odds on you smooth calling are therefore $5,400/$1,800, or 3-to-1. However, as I understand it, the implied odds are $5,400 (existing pot) + $1,800 (to call) + 2 x $3,400 (to raise all-in and get matched) = $14,000 (or double your stack) to $5,200 (call + raise all-in) = 35-to-13 or 2.7-to-1.

Since you are getting better odds on your money by calling, plus it gives you the option of re-assessing the situation after the turn, I would only call.

Thoughts?

[DoctorWard]

Assuming that my analysis above it correct, I see it is directly relevant what the level of blinds are for whether you call or not. If the blinds are $300-$600 (as per the above example) then a call receives 3.00-to-1 odds, while an all-in raise receives only 2.69-to-1 odds.

If the blinds were $400-$800, then a call would receive 3.00-to-1 odds. This is because pre-flop your opponent raises to twice the big blind, or $1,600. On the flop you bet the minimum of $800 and he raises $3,200 which is the pot-size pre-flop. Therefore, the pot was $1,600 + $1,600 (pre-flop) then $800 + $3,200 (to this pot), or $7,200. The pot odds on you smooth calling are therefore $7,200/$2,400, or 3.00-to-1.

For an all-in re-raise the implied odds are $7,200 (existing pot) + $2,400 (to call) + 2 x $2,200 (to raise all-in and get matched) = $14,000 (or double your stack) to $4,600 (call + raise all-in) = 70-to-23 or 3.04-to-1.

Since now you are getting better odds on your money by re-raising all in, I would not call when the blinds are $400-$800 but move all-in.

This is a probability question, can any one shed some light on this?

[ratso]

Depends on what the win means and how many slots it takes to be in the money. At a 10/1 single table, I would take a chance. It does not matter if he/she has top pair or a set at this point. I (you) need the straight (probably 8 outs). I go all in and take thke the shot. If it is a bigger stakes and bigger juice I would do something different depending on my eval of the player I am against.

[DoctorWard]

This is a $10+$1 single table tournament and not a cash game!

Mathematically what is the optimal solution assuming your opponent has the nuts (i.e. Kd-Kh) after the flop?