Stud Question

[David Sklansky]

Playing headsup 100-200 $25 ante, $25 bring in. Opponent opens with 5c showing. You make it $100 with ace of clubs showing and 9h 3s in hole. He calls. (Assume he will never reraise with anything.)

On the turn you catch th Ad and bet 200 into his Jh 5c. He raises 200. You are positive he will do this with trips and two pair every time and never with anything else. You know a reraise bluff won't work. Should you call if you are all in? What about if you are not?

[Mano]

There are 6 ways your opponent could have trips and 9 ways he could have 2 pair. If he has trips and you call all the way, you will win about 11% of the time. If he has 2 pr. and you call all the way you will win about 44% of the time. By my calculations this makes you about a 2.25:1 dog. The pot is laying 4.25:1, so if you would be all in this is a clear call. If you have enough money to call all streets you are getting about 1.8:1 odds, neglecting implied odds. Since you really can't bet your 2 pr., and you will probably only get extra bets if you catch an Ace on the river , aded to the possibility that you catch a third Ace and your opponent fills, I think this would be a fold.

[Rockfish]

The way I see it, if you call your last $200 to go all in it's 3:2 he's got two pair if you've seen no other cards.

EDIT: I see now that he could be rolled up and have not raised on 3rd street. This is a 424:1 shot. If you assume he started with a pair, it's 3:2 he's now got 2 pair. END EDIT

If it's head's up there should be $850 in the pot at the point you have to make the decision whether to go all in. That's 4:1 or better on your call with two chances to make a second pair or trips with your aces.

Heads-up going all in I call.

If you are not going all in with the call frankly I'm not sure. I might be inclined to check and call to the river and call if I make two pair and fold if I don't.

Rockfish

[Ignatius]

C(6,2)=15 combinations for his holecards. 6 for trips, 9 for twopair. Simulation gives:
.
<pre><font class="small">code:</font><hr>
Twopair: Ad-Ac-9h-3s: 44.6% 4:5
Js-Jh-5d-5c: 55.4% 5:4
Trips: Ad-Ac-9h-3s: 10.9% 1:8
Js-Jh-Jd-5c: 89.1% 8:1
</pre><hr>
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All-in szenario:
pot $1050, cost $200, EV = $126.70 so a clear call.
.
Naive call-down szenario (opponent always bets, I always call):
pot $2250, cost $800, EV = -$99.93, so you'll lose 1/2 a bet. But
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- you can muck and save $200 if you don't improve until the river. This alone improves your EV to -$99.93+0.44*$200 = -$11.93
- you see if your opponent improves on 5th or 6th street and can get away from an unimproved pair
- he cannot see if you make aces up
- you will be able to make an additional bet if you make trip aces on the river
- you will be able to make an additional bet for an EV of (0.6-0.4)*$200=$40 if you make aces up
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This is more than enough to make up for the 1/2 bet lost in the naive calldown szenario, so you have a clear call.

[Mano]

You may very well be right, just a couple of questions:

- you will be able to make an additional bet for an EV of (0.6-0.4)*$200=$40 if you make aces up

Aren't you neglecting the possibility that you will be reraised if your opponent has trips?

- you will be able to make an additional bet if you make trip aces on the river

Do you need to take into account that your opponent could fill on the river?

Again, not certain which is correct, but it seems less clear cut to me than you stated.

[Ignatius]

Aren't you neglecting the possibility that you will be reraised if your opponent has trips?
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I do. But just because Sklansky stated
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Assume he will never reraise with anything.
.
Otherwise you would of course be correct.
.
Do you need to take into account that your opponent could fill on the river?
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The probability that the last card makes you trips and fills him up seemed low enogh to ignore. After all, it's not a close decision as simply calling him down and mucking an unimproved pair at the river in already almost break even. All other 'buts' in the lists only need to make you $12 extra to make calling +EV.

[Mano]

I thought the "Assume he will never reraise with anything" statement was just for the flop (so you couldn't rule out the opponent being rolled up), and did not apply to the rest of the hand (especially since he raised on 4th street). If he will never raise for the rest of the hand, regardless of what you do and what hand he hits, then this certainly would be much more favorable for a call. If not, it could turn your $40 EV bet with 2 pair ((.6 - .4)*200) into a -$40 (.6*200 - .4*400) EV.

As for filling on the river, if all his cards are live your opponent will get a full house or quads on the river about 13% of the time when you get trips (about 8% when he has 2 pr. and 20% when he has trips). So, yes, river bet still would have large +EV when you get trips.

I think this hand depends heavily on if you can assume no raises or not.

[Ignatius]

Even if you assume no raises from either player for the rest of the hand, calling is still +EV, as the mere fact that you can get away from the hand if he fills up on 5th or 6th street will save you more than $40. In comparison, the fact that he might get away from twopair if you make open trips is almost worthless to him (less than $10) as it is (a) more than 3 times less likley to happen (4 vs. 2 outs, and he is pot stuck with trips) and (b) he would get almost correct odds to chase.