5 card draw logic problem (Poker)

[MJ4H]

This puzzle appears in Mike Caro's Draw Poker section of Super System by Doyle Brunson. If you've read this book or know this problem from elsewhere, give those who haven't a chance before you jump in with the answer.

You are in 1st position and have sandbagged three jacks, an Ace and a Queen. The player in 2nd position opens: everyone else passes. You raise. The Opener calls the raise and is all-in (he has no more chips so no betting can take place after the draw). You're about to ask for cards when the Opener spreads his hand on the table apprehensively.

"I wonder if I have you beat going!" he sighs.

You look at two Kings, two Queens, and a Jack. You hope he doesn't figure you for Trips because, based on past experience, you know he usually throws away his smaller Pair and draws three against what he thinks is Three of a Kind.

How many should you draw and, specifically, why?

Your hand:
http://www.cox-internet.com/pwatts14/hand1.bmp


Your opponent's hand:
http://www.cox-internet.com/pwatts14/hand2.bmp

[QuikSand]

I own the book, but haven't read the draw poker section... so I'll give it a shot, expecting to be wrong, though.

I think I would keep the ace and draw one card to my three jacks. I already have the lead on him however you put it, and whether he draws to his two pair (one draw to get three outs) or draws three to his kings (three draws to get three outs) I'm the favorite. Seems to me that drawing only one, and representing two pair, is the right play -- pushes me from favorite to heavy favorite. My likelihood of improving on the draw is secondary, it seems to me.

[MJ4H]

This is not the correct answer, nor the correct reasoning. Incidentally, Caro says in this section that there has only been one person to ever give him the correct answer and reasoning to this question *without hesitation*. Doyle Brunson.

[Comey]

I'd say none...make him think you have a straight, even with his great hand, it'll make him think twice.

I'm not a novice in poker, but in poker strategy. So, take it for what you will (which is probably the wrong answer) ;)

[QuikSand]

If you stand pat, wouldn't the logical thing for him be to draw to his two pair, hoping to boat? Sinced there's no more betting to be done, the only thing that matters is who ends up with the best hand at the end. I guess that supports the same end that I was leading toward - you want him to draw one, not three cards.

So, I'm guessing that's not what Caro's looking for.

[SirFozzie]

Draw one, keeping the Queen and showing the Ace.

Why? If you show the queen on the draw, he'll dump his queen set (1 out left), which you don't want. If you dump the ace, he'll figure his pairs of Kings And Queens are tops (not knowing you have a trip set), and he figures you for a straight or a flush draw.

[QuikSand]

If youu dump your Q, as I originally suggested, are you obliged to show it?

[QuikSand]

...though I'll confess that Sir Fozzie's has the ring of a "right" answer to me. BY showing that you don't have aces in youur possible two pair, he should think that he has you beat with any hand that you'd keep four cards for. He should draw just one, which is what you want. Seems fair enough, to me.

[MJ4H]

No.

[finkenst]

keep the three clubs and go for flush/royal.

[Brillig]

Your opponent has two realistic choices - draw one (7% chance of filling up) or draw three (14% chance of making trips). (I'm going to ignore edge cases like your opponent drawing three and making a lower full house that jacks-full can beat...)

You have three choices - draw none, draw one (7% chance of filling up), draw two (7% chance of filling up). If you fill up, you beat his trips but lose to a full house from your opponent.

Given your small chance of improvement, your most significant edge lies in maneuvering your opponent to draw one rather than draw three. Even if you fill up, it only is to your advantage if your opponent draws three... the one thing you don't want him to do!

Based on the problem, this means that you want to convince your opponent that you have anything but trips. Drawing two is obviously the worst idea.

Drawing one or drawing none each have some attractive points. If you draw one, you're representing two pair (or quads :) ), drawing none, a pat hand. Either way, it seems better for your opponent to draw one - so the edge has to be whether your opponent is more likely to read you as disguising trips if you draw one or none.

You give up a relatively small edge drawing only one to trips, so this your opponent is much more likely to read you for trips if you draw one rather than standing pat.

Stand pat.

[MJ4H]

Just for argument's sake, if you were to draw one card, what card(s) would you be hoping to get?

[Brillig]

It hardly matters - logically, you'd draw one to JJJA, hoping to fill up which would beat the outlier cases where your opponent draws three to KK and gets a lower full house.

In reality, the only reason to draw one is if you believe your opponent is more likely to read you for trips if you stand pat than if you draw one - admittedly unlikely unless you are dealing with a very sophisticated opponent (or one who's been peeking at your cards).

[NYFAN]

I can't say that this would make sense to me, but who knows, maybe the probabilities work out right in this case...

What if you drew 2, and showed a Jack and a Queen - holding the Ace, but obviously breaking up your 3 of a kind. The logic would be as follows:

You hope to pull 2 aces to give you Aces over Jacks (which would beat anything he had unless he pulled 4 of a kind kings), but more importantly you hope to break up his two pair to force him to go for the straight. By throwing down a Jack and a Queen, he's going to figure that you either have 3 Aces, or that you are going for a lower full house (something low over whatever you draw) or straight - once again probably low. As a result he may go for the high straight, knowing that at least 3 Queens and 2 jacks are out of play, and not knowing that any aces are in play, he may feel that his chances of getting an Ace and a 10 or a 9 and a 10 would be higher than getting two kings (since you showed the Queen he's definitely giving up on them), and with probability he may be right. But if he got nothing he would be beat (by a pair of jacks) and if he got his straight, he would still be beat if you got your 2 aces.

[NYFAN]

bump

[MJ4H]

Answer below
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You should draw none! Since the opener has a J, you can't make quads. If you draw one, there's a chance the opener will think you're disguising trips and will draw-down to his pair of kings. If he draws three to kings, he has a better chance of beating your 3 jacks than if he draws one. If you draw two, he will certainly figure you for trips and draw three. After all, you raised. If you stand pat, though, he will be forced to take his best shout at beating a pat hand, which is to draw one, hoping to make a full house.

A key point here: If you draw, you can't effectively help your hand if he draws one also. And if he draws three, he's cutting into your win-probability.

The reason you can't help if he draws one is that Jacks-full is no better than three jacks against his full house. If his one-card draw gives him a full house, it will be queens full minimum. That beats jacks full and you can't make quads since he holds the case jack. It doesn't matter whether you keep the ace kicker, the queen kicker, or draw two because you can't make any meaningful improvement against his one-card draw, and it's mathematically to your advantage for him to draw one.

Stand pat.

[Comey]

So, I was right with the decision...just the logic was off. I can accept that.