An interesting NL problem to get you thinking...

Hi

I usually lurk in the LHE thread, but I have come over to the dark side (lol) for an interesting, semi-tricky hypothetical question.

Lets suppose the following.

It’s Heads-up NL and each player has $1000 (this is cash, not a tourney)
Pre-flop the SB raises to $50 and the BB calls. That’s $100 in the pot
For some reason you both agree to flip your hands up pre-flop, but still play out the hand

Player A has JcJs and Player B has JhJd
The flop comes 10c, 2c, 4c

Yet to come is a post-flop bet, turn card, possible turn bet, river card, and possible river bet.

The question is who wins the pot (or is it split), and how much is the pot when it is taken down? I believe there is only one correct answer, assuming that both players are very good and know what they are doing.

I’ll post the answer later, but I’m sure someone will come up with it in the meantime.

PS. If you have seen this one before and are absolutely sure of the answer, it might be better if you did not post so that others could work it out. If you have not seen this before, then go for it

Player B has no outs to win, and has to dodge 9 cards twice to split. (the remaining clubs.)

Therefore 65% of the time the pot will be split and 35% Player A wins.

Player B must fold to any bet by Player A.
So, Player A wins $50

Depends on who is in what position.

2 possible plays.

1. Player A w/ Jc is on button, flop comes and player B bets out with his overpair, Player A will now assume that Player B Has at best TPTK because if he flopped the flush he would check to entice a bet. Player A will then Raise All in believing that he has any board pair beat and his flush outs arent dead.
Player B will be faced with the massive raise and will probably fold, not wanting to gamble his entire stack.

This could be altered depending on how long the heads up match has been going {not specified}, the earlier in the match, the more likely it is that Player B will fold.

2. Player B w/o Jc is on button, flop comes and Player A bets out with his overpair and 4-flush. Sounds similiar right? This time Player B will almost invariably make a massive raise, both will wind up allin. Then we're back to percentages.

I believe there is only one correct answer

I don't believe there is ever ONLY 1 answer.
To many external variables that cant be controlled (e.g. moods).

A has a chance to make a little bit more money. if player A just bets a buck, player B is getting odds for a refund. I think player A needs to bet 9/47 * $50 to give coinflip odds on B's fifty bucks. Then, if the club misses A needs to bet 9/46 * 50 + ~$10 (the 9/47*50) to give coinflip odds on B's hand to see the next card. i don't see any point in betting on the river, if A gets the flush, it's over.

As far as A is concerened, the worst that can happen is a split pot, but with a really small bet A gets a coinflip for more of B's money.

Originally Posted by whileone

As far as A is concerened, the worst that can happen is a split pot, but with a really small bet A gets a coinflip for more of B's money.

I disagree, there is very little chance that Player A put player B on JJ. therefore he could be worrying about a small 2-pair, possible set, or maybe even the flush.

Originally Posted by ArcticKnight

For some reason you both agree to flip your hands up pre-flop, but still play out the hand

this might make my reasoning a little more clear

Originally Posted by Aceofone

Depends on who is in what position.

2 possible plays.

1. Player A w/ Jc is on button, flop comes and player B bets out with his overpair, Player A will now assume that Player B Has at best TPTK because if he flopped the flush he would check to entice a bet. Player A will then Raise All in believing that he has any board pair beat and his flush outs arent dead.
Player B will be faced with the massive raise and will probably fold, not wanting to gamble his entire stack.

This could be altered depending on how long the heads up match has been going {not specified}, the earlier in the match, the more likely it is that Player B will fold.

2. Player B w/o Jc is on button, flop comes and Player A bets out with his overpair and 4-flush. Sounds similiar right? This time Player B will almost invariably make a massive raise, both will wind up allin. Then we're back to percentages.

I believe there is only one correct answer

I don't believe there is ever ONLY 1 answer.
To many external variables that cant be controlled (e.g. moods).

You missed the part where I said they both show thier hands to each other pre-flop. Neither play has to "assume" what the other player has.

my apologies, I missed that.

Then it is a very basic mathematical question.

~3:1 Player A wins.
~3:2 it is split

The question is who wins the pot (or is it split), and how much is the pot when it is taken down? I believe there is only one correct answer, assuming that both players are very good and know what they are doing.

More than likely both players are allin on the flop. 2000$ pot.

Player A = player with club
Player B = player without club

I think if you assume each player is acting rationally and anticipates rational decisions from the other, player B will check if he is first to act, and player A will move all-in if he is first or second to act. Player B will then fold in turn.

The reasoning is that player B can expect player A to move all-in to maximize his own chances of winning the pot without risking anything, and so player B minimizes his own losses by checking since he cannot sensibly risk his entire stack when the best he can do is break even.

Originally Posted by dsaxton

Player A = player with club
Player B = player without club

I think if you assume each player is acting rationally and anticipates rational decisions from the other, player B will check if he is first to act, and player A will move all-in if he is first or second to act. Player B will then fold in turn.

The reasoning is that player B can expect player A to move all-in to maximize his own chances of winning the pot without risking anything, and so player B minimizes his own losses by checking since he cannot sensibly risk his entire stack when the best he can do is break even.

no, the best player B can do, is win $50 bucks. Once it's in the middle, it shouldn't be counted as part of his stack. If player a bets $1, B *has* to call, because it's +EV he could win $51 for a $1 bet. he has odds for that.

It's player A's job to bet as much as B will call so if he catches the club, he can make a few extra bucks. B won't make a -EV decision, so the worst odds A can offer are 38:9. B has a share of that pot, by not calling a small enough bet, he's donating money to A's cause.

I think you guys are thinking to literally im assuming, by the way he worded his post, that this is some kind of trick question, a riddle. He even says " I believe there is only one correct answer"

there is no trick, just common sense

Originally Posted by whileone

Originally Posted by dsaxton

Player A = player with club
Player B = player without club

I think if you assume each player is acting rationally and anticipates rational decisions from the other, player B will check if he is first to act, and player A will move all-in if he is first or second to act. Player B will then fold in turn.

The reasoning is that player B can expect player A to move all-in to maximize his own chances of winning the pot without risking anything, and so player B minimizes his own losses by checking since he cannot sensibly risk his entire stack when the best he can do is break even.

no, the best player B can do, is win $50 bucks. Once it's in the middle, it shouldn't be counted as part of his stack. If player a bets $1, B *has* to call, because it's +EV he could win $51 for a $1 bet. he has odds for that.

It's player A's job to bet as much as B will call so if he catches the club, he can make a few extra bucks. B won't make a -EV decision, so the worst odds A can offer are 38:9. B has a share of that pot, by not calling a small enough bet, he's donating money to A's cause.

I don't think this is necessarily the better route. If he makes medium-sized bets, it is true that he allows for the possibility of winning some extra money, but he also allows his opponent the option to correctly pursue a split pot. If he moves all-in, he forces player B to give up the pot immediately, or risk his whole stack in the hopes of winning $50. There's probably at least some element of personal preference here, but I think the latter choice is better for player A.

Player A wins either on the flop or the turn. It appears that Player A can make a small bet on the flop to get Player B to chase, but Player B realizes that he may never see the river since Player A can push on the turn no matter what card falls and must fold to any flop bet.

Player A could increase his variance by checking the flop and betting about 2/3 of the pot on the turn (17.5/26.5 I think). Any larger bet and Player B will fold. Any smaller bet and Player A is costing himself money.

Edit: After reflection, I think the amount Player A must bet on the turn after checking the flop is actually around twice the pot (17.5/9*P or about 194.44). This would give Player B pot odds of 26.5:17.5, which he can call with EV 0. The expectation for Player A is 100 whether B calls or folds to the bet.

"there is no trick, just common sense " AHA that proves even more that it is a riddle of some sort

I think player A wins 100 dollars on the flop every time.

Player B knows even if player A makes a small bet that would make sense to call, A will push the turn anyway, and now B would've lost x amount extra for calling the flop because he has to fold to a turn push.

i just realized koolmoe already said this in so many words. oh well.

Hi

A few folks posted what I think is the only correct answer.

Player A takes down the Pot for the $100 that is already there.

Here is the reasoning. Player A can win with a flush, or he can tie if he misses the flush; Player B can only tie the hand – he cannot win.

With that in mind, there is no use trying to figure out what size bet is acceptable for player B to call post-flop (as many of you have tried to do) . The fact is Player B should fold to any post-flop bet (even $10).

Why, because if Player A hits the flush on the turn, player B loses $60 dollars (instead of $50). That is obvious. But if player A misses the flush on the turn , he will go all-in for $940 after the turn, and Player B will have to fold. Player B would be putting up $940 with around an 80% chance of getting his $60 back, and around a 20% chance of losing $940. Because Player B can never do better than getting back exactly what he put in, he must fold to a large all-in bet.

Player B has to be smart enough to know that whatever Player A bets post-flop, it’s just a trap for an all-in on the turn if he misses the flush. In short, Player B is screwed.


NOTE: If Player B is not thinking clearly, he could be sucked into a $25 or $50 bet post-flop (reasoning that he has correct odds), but not thinking ahead to the all-in that will be sure to follow.

What I wonder is how many players in Player B’s position would actually think this through, and how many would make an incorrect call post-flop.

ok ok fine it wasnt a trick question! I was waiting for the

PLAYER B WINS $867 FROM PLAYER A!!! WHAT WHAT WHAT!

Player B bets 867$ on the flop, Player A, being a seeing eye chimp with no knowledge of poker folds. (Of course other chimps are poker gods just not this one)

I think if Player A waits for the turn to move all-in, he takes too much of a risk of splitting the pot. Player B may just decide to gamble and call since the pot will be split a large percentage of the time.

i'm the only one to consider that B might call something, i'm the chump.

Just so i'm clear,
A must go all in, to protect his share of B's blind before the flop.
If A just checks to the river then B might split the pot, which is bad.
I suppose any bet by A is too scary for B to call on the flop, because there are still two cards to come, but a small bet on the turn I think is callable.

B cannot call under any circumstance regardless of bet size. He has nothing to win beyond what he puts in regardless of the final 2 cards.

Originally Posted by vfreeman

B cannot call under any circumstance regardless of bet size. He has nothing to win beyond what he puts in regardless of the final 2 cards.

Well, in a sense Player B "expects" to win a fraction of half of the pot on each street, since the pot will be split a percentage of the time. Strictly in terms of expected value, it may make sense to call, for example, a $1 bet on the flop, since the majority of the time the player will be returned much more.

Player A goes all in and player B goes all in. Why? Because it's on party poker and man, pocket jacks....that's a pretty good hand!

Originally Posted by TylerK

Player A goes all in and player B goes all in. Why? Because it's on Party Poker and man, pocket jacks....that's a pretty good hand!

LOL, and Player C called the preflop raise with 3c8s and calls the AI on the flop and hits 5c on the turn and 6c on the river to take it down. Everyone else is dumbfounded as Player C struts his stuff thinking he's gonna be the next Gus Hansen.