A 5 card draw poker puzzler courtesy of Mike Caro

BobSloane

This was in super system so some of you have probably seen it before.

"There's a favourite poker problem I devised to test people.Only one person has ever given me the answer without hesitation. This is the problem:

You are in first position and have sandbagged 3 jacks, an Ace and a queen. The player in second 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' he sighs.
You look at 2 Kings 2 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 3 against what he thinks is three-of-a-kind. How many cards should you draw, and specifically, why?"

NickyOD

none, obviously. if he puts you on a made hand he will draw one card to try and make the full boat which you wouldn't be able to beat by drawing 2 anyway

ITT-Pat

definately draw 1 card so hopefully he'll put you on 2 pair also. This will make hesitate to draw 3 cards. With a little luck, he might put you on a Big Draw like 10hJhQhKh(maybe he'll think this is why you didnt open?).

If he puts you on a big draw, then he wont want to put down his 2 pair for fear that you might draw a lucky pair of Kings and have a better kicker than him.

NickyOD

ITT-Pat wrote:

definately draw 1 card so hopefully he'll put you on 2 pair also. This will make hesitate to draw 3 cards. With a little luck, he might put you on a Big Draw like 10hJhQhKh(maybe he'll think this is why you didnt open?).

If he puts you on a big draw, then he wont want to put down his 2 pair for fear that you might draw a lucky pair of Kings and have a better kicker than him.

I thought about that too but people often draw 1 to disguise trips and he could smell that, but you would almost never stand pat with them. Also since the villain has shown his hand and you decided not to draw, he has to believe his only chance of winning the hand is to make a full house.

ITT-Pat

Although the time of my post suggests otherwise, i posted it before i seen yours, so my "definatly draw 1 card" remark wasnt meant as a contradiction to your post, nicky.

Anywho, although i do see your point of standing pat, he could still easily see a decision of standing pat, as a hidden 2 pair that contains Aces just as much as he would see drawing 1 card as a hidden trips.

I think the situation is very dependant on the opponent and whether you think your oppenent could envision you not opening and then re-raising with a big draw.

sickpuppy

You draw 2cards not sure of the odds but if he draws 3 to his kings he need to hit trips or better to win.So with 3 card sto come hes a 1 in 8 chance of hittinga king or a little smaller for him to get trips with his 3 discards.I f he asks for 1 card he has 4 outs to fill his boat and hes the lone jack u need so if he fills ahouse u are drawing dead.so hes 4 outs out of 42 cards left in deck presuming were hu so hes a 10.5 to 1 shot so odds dictate u draw 2 cards i think.

ITT-Pat

never draw 2 cards in this situation

sickpuppy

Are my odds wrong pat explaian yourselfif you can please i dint think it out fully.Just what came into my head .

NickyOD

sickpuppy if he knows you have trips he will know his best chance to win the hand is to draw 3 cards. You want to make him tihnk drawing 1 cards is his best option. Since your hand cannot improve to win then drawing 2 is your worst option.

Cuban Son

If the guy decides to draw 3 he is only drawing to 2 outs to beat you. If he is decides to draw 1 card he has 3 outs to beat you as you have one of his queens.
There is no point in drawing any cards here because he has your fourth jack and you have one of his outs.
The likelyhood is you are holding your strongest possible hand JJJAQ.

ITT-Pat

I just re-read the 1st post and only know realise that the case jack is already in his hand so you've got no chance of impoving your hand.

So as your only goal in this hand is for hin to draw one card, i agree with nicky and say stand pat

As far as the maths goes, you definately want him to draw 1 card so he'll have 3 outs once, rather than 2 outs twice(the equivalent of 4 outs)

sickpuppy

Bollox im blind didnt see we have the case jack in our hand as well.So i agree with nicky ask for 1 card as he has 3 outs.My maths need some major adjustment

NickyOD

sickpuppy wrote:

Bollox im blind didnt see we have the case jack in our hand as well.So i agree with nicky ask for 1 card as he has 3 outs.My maths need some major adjustment.

nah, I think standing pat is the answer. If the villain thinks theres a chance he could end up drawing 3 cards against a made hand then he'll surely decide against it.


If he draws 3

((2/42)+(2/41)+(2/40))*((3/42)+(2/41)*(1/40) (He can also draw the 3 remaining aces to win but it doesn't make any difference to the percentages)

or

(.0476 + .0489 + .05)X(.0714 X .0489 X .0244)

which is a 14.65% chance of winning if he decides to draw 3 cards.

If he draws one. (4/42)

9.5% chance of winning.

So its best that you do what you can to get the villain to draw one card.

ITT-Pat

NickyOD wrote:

nah, I think standing pat is the answer. If the villain thinks theres a chance he could end up drawing 3 cards against a made hand then he'll surely decide against it.


If he draws 3

((2/47)+(2/46)+(2/45))*((3/47)+(2/46)*(1/45) (He can also draw the 3 remaining aces to win but it doesn't make any difference to the percentages)

or

(.0426 + .0435 + .0444)X(.0638 X .0435 X .0222)

which is a 13% chance of winning if he decides to draw 3 cards.

If he draws one. (4/47)

8.5% chance of winning.

So its best that you do what you can to get the villain to draw one card.

Well Said

sickpuppy

I see you have aformula for getting the odds but should it not be for 42 cards not 47 as we both have 5 cards in hand. Regardless standing pat or smoking as used be called in days gone bye or drawing one card whatever gets villain to draw 1 card is our best option just the odds would be alittle different if you were using 42 cards not 47 .

NickyOD

sickpuppy wrote:

I see you have aformula for getting the odds but should it not be for 42 cards not 47 as we both have 5 cards in hand. Regardless standing pat or smoking as used be called in days gone bye or drawing one card whatever gets villain to draw 1 card is our best option just the odds would be alittle different if you were using 42 cards not 47 .

Ah yeah you're right. Wow, that was dumb.

I'll change it.

poorbarman

As some one who played an awful lot of draw i would definately stand pat in this situation.you want him to draw only one card as nickys complicated :rolleyes: maths answer implies.

BobSloane

"You should draw none! Since the opener has a jack you can't make 4 of a kind. If you draw one there's a chance the opener will think you're disguising trips and draw down to his pair of kings. If he draws 3 to kings he has a better chance of beating your 3 jacks than if he draws one. If you draw 2 he will certainly figure you for trips and draw three.If you stand pat though he will be forced to take his best shot at beating a pat hand, which is to draw one hoping to make a full house.

A key point: 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 four jacks since he holds a 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 its mathematically to your advantage for him to draw one.

Stand pat.

If the analysis seems complicated its because the logic is difficult. But, don't worry about it.
In case you're curious who solved that problem without hesitation, it was Doyle Brunson."



Wp Nicky. I must now admire your poker logic along with your swollen testicles.