Another Fourth St. Decision

[pudley4]

9 ways to have AQ without Qd.
3 ways to have AQ with Qd.
3 ways to have AJ with Jd.
3 ways to have KQ with Qd.
3 ways to have KJ with Jd.
1 way each for QdJd, Qd9d, Jd9d.

So 9 ways where you want to get the 3rd player out, and 15 ways where you want him in.

My calculations show you should always raise, regardless of the pot size, but I need to double-check.

[pudley4]

1-Your opponent could have 24 possible hands.
9 AQ w/out Q [img]/forums/images/icons/diamond.gif[/img] (Call these Hand 1)
3 each AQ w/Q [img]/forums/images/icons/diamond.gif[/img] , AJ [img]/forums/images/icons/diamond.gif[/img] , KQ [img]/forums/images/icons/diamond.gif[/img] , KJ [img]/forums/images/icons/diamond.gif[/img] (call these Hand 2)
1 each Q [img]/forums/images/icons/diamond.gif[/img] J [img]/forums/images/icons/diamond.gif[/img] , Q [img]/forums/images/icons/diamond.gif[/img] 9 [img]/forums/images/icons/diamond.gif[/img] , J [img]/forums/images/icons/diamond.gif[/img] 9 [img]/forums/images/icons/diamond.gif[/img] (call these Hand 3)

2-There are 42 remaining cards in the deck.

3-The pot size after your opponent bets is X

(For simplicity's sake, I will not be dividing by 24 for the total number of hands, or by 42 for the total number of river cards. I will also be referring to bets instead of dollars)

Hand 1
If your opp has Hand 1, he is drawing dead if you raise. If you just call, your other opp can draw out on you 8 times. So your EV for a raise is 42(X+1) (42 cards on the river give you a win, so you win the pot, X, plus 1 bet). Your EV for a call is 34(X+1)-8(1) (34 cards give you the win, 8 cards cost you the 1 bet you called.)

Hand 2
Notice that in Hands 2 and 3, your other opponent is drawing dead, so you win or lose the same number of pots regardless of whether he is in the hand or not. Obviously you'll want him to stay in, because in these cases, you'll be winning the same amount of money while risking less.

In Hand 2, you'll win 35 times and lose 7 times no matter what you do. Your EV for a raise is 35(X+1)-7(2). Your EV for a call is 35(X+1)-7(1).

Hand 3
In Hand 3, you'll win 10 times and lose 32 times no matter what you do. Your EV for a raise is 10(X+1)-32(2). Your EV for a call is 10(X+1)-32(1).

Now, calculate the EV of a raise:

Hand 1 + Hand 2 + Hand 3=9(42X+42)+12(35X+21)+3(10X-54)=828X+468

Calculate the EV of a call:

Hand 1 + Hand 2 + Hand 3=9(34x+26)+12(35x+28)+3(10x-22)
=756x+504

We want EV(raise)>EV(call), so 828x+468>756x+504. This is true for all X>1. Remember that X=pot size after your opponent's bet, so regardless of the pot size before the turn, as soon as he bets, you raise.

(I hope my math is right) [img]/forums/images/icons/laugh.gif[/img]

[HiatusOver]

I disagree with those who say you should always raise, I think most people here are off-base. You are investing an extra $20 dollars to fold the 10d...more than half of the time the 10d will be drawing dead, so you obviously will have wasted money in these situations...on top of that, the 10d will only hit a non-board pairing diamond 8 out of 44 times WHEN IT IS DRAWING LIVE (which is only about 40% of the time). Because of these two facts, it is CLEARLY not worth it for you to invest the extra 20 dollars here in a small pot of let's say $80 because the 10d will not beat you anywhere close to 1 out of every 4 times.

[Poker blog]

I'm gonna reply to my own post. I am on crack. Actually, the real problem was that it was 6am in the morning and I still hadn't gone to bed yet. Now that exams are almost over, I'll get a chance to think about it.

I actually thought I had a caveat about how I hadn't slept and couldn't think straight in my original post, but I didn't. It's the crack, I guess.

[cero_z]

By my gorilla math, calling makes about $24/play, and raising makes $35/play, so I think you should raise regardless of pot size. Given the wording of the question, this seems wrong, so I look forward to a human helping out where apes have failed.

[HiatusOver]

This will be my last post under this topic until we get an answer, but I think I found the error in my previous reasoning. Because you are ahead in most on the scenarios, investing the extra $20 dollars does not actually "COST" you $20 dollars and in fact it costs you much less...therefore my previous posts were way off...i think

[woodman]

according to the question call & raise only options. Also, the only time the twit comes into play is when the first guy is drawing dead, hence:

(9/24)*(36/43)*pot size should be greater than the extra $20 to nock out the twit

Therefore pot above $63.70 raise, below, let the twit play.

[deadbart]

It doesn't cost you $20 to knock out the twit, since you win most of the time. Thus, the pot can be much smaller than your result.

[woodman]

correction, twit has 8 flush outs when no. 1 is drawing dead:
9/24*35/43*pot size>20
hence for a pot size less than $65.52 let the twit play otherwise raise

[woodman]

its a matter of giving the 2nd guy the correct odds to call or not, hence his odds of winning determine the correct pot size. so i'll stand by my answer......for now