Interesting Hypothetical?

[ML4L]

Hey all,

This one just popped into my head, and I thought that some of y'all might enjoy thinking about it...

$10/$20 pot-limit hold 'em heads-up where both players turn their cards face-up once the flop comes down. Stacks are $2000 each. Pot is unraised preflop. Flop comes:

T /images/graemlins/spade.gif7 /images/graemlins/spade.gif2 /images/graemlins/diamond.gif

Player A tables 9 /images/graemlins/spade.gif8 /images/graemlins/spade.gif. Player B tables A /images/graemlins/heart.gifA /images/graemlins/diamond.gif.

1) What is the optimal strategy for each if A is first to act?

2) What is the optimal strategy for each if B is first to act?

The answers might be obvious; haven't given it much thought yet... I feel like there might be some practical applications for the theory behind the answers, but I haven't tried to figure that out yet either... We can all work through it together (or, everyone else might find it boring/stupid, in which case, the thread will just die).

ML4L

Edit: For more fun, here is another wrinkle:

3) How does the proper strategy for each player change if the game is no-limit rather than pot-limit?

[Yeti]

Unless I'm missing something, this seems pretty simple. It's a nice change of pace though.

Will reply later, I can't 4-table like I used to /images/graemlins/frown.gif

[amoeba]

player A should bet enough so that his remaining stack is correct to draw to a 15 outer should the turn miss.

I'm not sure about player B situation. I would say bet enough to make drawing to 15 outs on the turn incorrect and pushing a blank turn.

[SpaceAce]

[ QUOTE ]
player A should bet enough so that his remaining stack is correct to draw to a 15 outer should the turn miss.

I'm not sure about player B situation. I would say bet enough to make drawing to 15 outs on the turn incorrect and pushing a blank turn.

[/ QUOTE ]

If we assume that both players are aware of the odds and only want to make plays with positive expecttaion, I think your line is wrong. Here's my thinking:

Player A should know he's about a 55/45 (wait... Twodiming it... .563/.437) favorite on the flop. Player B should also be aware of this. If Player A bets enough to make drawing to his outs on the turn correct, Player B probably wouldn't call because A) he's losing money on whatever he puts in on this street and B) he will be unable to force player A to make a mistake on the turn even if it is a blank.

As for the player "B" situation, no matter what B bets, A would just push over the top of him because he's a substantial favorite so B would never get a chance to push a blank turn.

Maybe there's a basic flaw in my reasoning but to me it looks like B should be check/folding and A should be pushing. That's just off the top of my head, though, so a more in-depth look would be nice.

SpaceAce

[Yeti]

[ QUOTE ]
Maybe there's a basic flaw in my reasoning

[/ QUOTE ]

This is pot limit.

[KaneKungFu123]

[ QUOTE ]
Unless I'm missing something, this seems pretty simple. It's a nice change of pace though.

Will reply later, I can't 4-table like I used to /images/graemlins/frown.gif

[/ QUOTE ]

[technologic]

in either case, the cards are face up, so there's no implied odds, correct? all the players can examine are immediate pot odds.

let's work backwards for a second.

assume players have made it to the river with significant money behind. this should go, whoever has the better hand will bet, and the other will fold. this is a very simple street.

assume players have made it to the turn with significant money still behind. if the flush or the straight made it, if player A were first to act, he would bet out and player b would fold. in the event that it was a deuce of spades, he would bet out an amount that was a bit greater than 1/10 pot, and if it was an ace of spades, he'd bet something a bit greater than 1/2.5 pot, whatever it is to make it incorrect to draw. any other card, he'd probably check call, other than one that paired the deuce or gave an ace with no spade.

for player B, he'd check fold any straight or flush card, and bet out any other card.

knowing that the action on the turn and the river are pretty straight forward, ie player A and player B have immediate odds in front of them and will only call when it pot odds dictate, let's examine the flop.

player A is ONLY a 5-4 favorite if he sees the turn and river cards. however, as we have determined, we have to play street by street. player A's main objective would be to pour all his money in on the flop, but player B knows this and can limit this, because it is pot limit. player A will bet out (40), player B will call (he is getting better than 5-4 on his money). then the scenarios above will play out.

if player B were to act first, nothing would change. player A is still the favorite, so there's no need to pour money into the flop. player B would check call a bet, and the scenarios would play out.

i THINK the theory is, if there are no implied odds, ie the turn and river cards will play themselves without any mistakes, any flop bet stands as if the two cards are dealt out already. since the straight flush is only a 5-4 favorite, there is no way he can bet out to make calling by the AA incorrect, since AA will always be getting 2-1.

i could be fatally wrong, so feel free to enlighten, mike.

in the third scenario, i'd imagine player A would just push or something similar.

[SpaceAce]

[ QUOTE ]
[ QUOTE ]
Maybe there's a basic flaw in my reasoning

[/ QUOTE ]

This is pot limit.

[/ QUOTE ]

Ugh, that would be a pretty basic flaw. I used to be able to read.

SpaceAce

[coltrane]

I'm assuming they both know the other is also playing optimally since their cards are face-up.....

1) if A (98s) is first to act, he should check, B (aces) should bet pot, A should call
2) if B is first to act, he should bet pot, A should call

the reason A should not raise in either case is because he knows that B is playing optimally.....and because of that, B knows not to get enough in the pot so that A is either all-in on the flop or has less than a pot-sized bet on the turn (the over/under on this is a third of their stacks on the flop).....essentially, A's equity is big on the flop, but he's a 2-1 dog from card to card (this could change depending on the turn card)......so, B would like to charge him more than 2-1 on the flop (only possible if A raises) while still being able to charge him 2-1 on the turn.....knowing this, A shouldn't even bother with a raise anywhere, he should just take the 2-1 being offered to him.....

3) if the game is no-limit, A would want to put in any amount greater than 1/3 of his stack on the flop, and B should fold!.....reason being, once A puts in more than a third of his stack on the flop, he guarantees getting better than 2-1 on the turn and locks in the 1.02-1 effective odds he gets for both cards.....knowing this, B should fold because he's a 1.29-1 dog with two to come......

any question that helps us understand equity better is interesting.....

[MVicuna]

Hi,

I must be missing something as this seems to easy.

1) A should bet the pot and B should call since B is losing money on this street and only 11 cards in the deck improve our odds enough to make a turn call of a pot bet by B incorrect so a raise on this street had -EV given only a 11:45 chance of chance of a +EV situation on the turn.

2) B should check and A should bet the pot.

3) A should go all in and B should check/fold.

Later,
MarkV.

[MVicuna]

I may have gotten this wrong.

1) 1 As, 3 Ts, 3 7s, 2 2s = 9 cards out of 45 that make it wrong for A to call the turn.

2) 3 ks, 3qs, 3 5s, 3 4s, 3 3s = 15 cards that make it ~EV for A to call.

3) 3 9's, 3 8's = 6 cards that make it 55/45 for A to call.

4) 3 js, 3 6's, 9 spades = 15 cards that make it wrong for B to call.

if they manage to bet exactly 2k on the flop.

1) 20% of the time A folds. B wins 1k.
2) 33% of the time A calls. B wins 2640.
3) 13% of the time a calls. B wins 2200.
4) 33% of the time B folds. B loses 1k.

So A has to get more then half of B's stack in on the flop in order for it to be profitable in the long run.

Thanks,
MarkV.