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ajmargarine
09-13-2005, 02:21 AM
Hypothetical NLHE Heads-up. Hero holds A /images/graemlins/diamond.gif A /images/graemlins/heart.gif.

The board on the turn reads T /images/graemlins/club.gif 6 /images/graemlins/club.gif 3 /images/graemlins/heart.gif 2 /images/graemlins/spade.gif

Action is on villian who flips over his cards revealing A /images/graemlins/club.gif K /images/graemlins/club.gif. Hero obliges and shows his AA also. So, they both know what the other has. Villian checks to Hero.

Pot is \$100. And both Hero and Villian have only \$20 behind. Which is the better play: Bet the \$20, or check behind?

Luzion
09-13-2005, 03:57 AM
[ QUOTE ]
Hypothetical NLHE Heads-up. Hero holds A /images/graemlins/diamond.gif A /images/graemlins/heart.gif.

The board on the turn reads T /images/graemlins/club.gif 6 /images/graemlins/club.gif 3 /images/graemlins/heart.gif 2 /images/graemlins/spade.gif

Action is on villian who flips over his cards revealing A /images/graemlins/club.gif K /images/graemlins/club.gif. Hero obliges and shows his AA also. So, they both know what the other has. Villian checks to Hero.

Pot is \$100. And both Hero and Villian have only \$20 behind. Which is the better play: Bet the \$20, or check behind?

[/ QUOTE ]

WTF? Are you joking? /images/graemlins/confused.gif

You bet the \$20 of course.

manpower
09-13-2005, 01:18 PM
Unless I'm misreading the question, I gotta go with:
[ QUOTE ]
WTF? Are you joking? /images/graemlins/confused.gif

[/ QUOTE ]

Mr. Curious
09-13-2005, 01:31 PM
[ QUOTE ]
Hypothetical NLHE Heads-up. Hero holds A /images/graemlins/diamond.gif A /images/graemlins/heart.gif.

The board on the turn reads T /images/graemlins/club.gif 6 /images/graemlins/club.gif 3 /images/graemlins/heart.gif 2 /images/graemlins/spade.gif

Action is on villian who flips over his cards revealing A /images/graemlins/club.gif K /images/graemlins/club.gif. Hero obliges and shows his AA also. So, they both know what the other has. Villian checks to Hero.

Pot is \$100. And both Hero and Villian have only \$20 behind. Which is the better play: Bet the \$20, or check behind?

[/ QUOTE ]

Basic assumptions:

Villian understands pot odds.
You understand pot odds.
Villian will not make a mistake in calling.
Villian will fold if he does not make his hand.
You fold if Villian does make his hand.

Villian has 9 outs (the /images/graemlins/club.gifs). There are 8 cards showing and 44 left in the deck. So Villian needs 32:8 or 4:1 pot odds to call correctly. With \$100 in the pot, we need to bet \$34 to give Villian exact odds to call.

From an EV perspective:

If we bet \$34 to win \$170 and we're a 4:1 favorite, we'll win \$170*4 and lose \$34*1 = 680-34=646 or 646/5 or 129.2

If we check behind, we never win anything extra when opponent misses and always lose \$100 when he does, so it comes out as 4*100 - 1*100 = 400-100 = 300/5 = \$60. So it is NEGATIVE EV for us NOT to bet the optimal amount because we win less in the long run.

OrangeKing
09-13-2005, 02:52 PM
[ QUOTE ]
With \$100 in the pot, we need to bet \$34 to give Villian exact odds to call.

[/ QUOTE ]

We're talking about limit though, so betting \$34 is not an option.

Of course the correct answer is to bet the \$20 anyway. The OP seems to have (or seems to be pointing out) a common misunderstanding of the relationsihp between pot odds and EV.

If we bet the \$20, the other player has the right odds to call, and neither player has made a mistake. However, you have gained EV, while the player on the draw has lost EV! The reason this occurs is that of the \$40 that has just gone in the pot (\$20 from each player), most of it - more than \$20 - will go to you, as your pot equity is up around 80%. The player on the draw would be much happier from a pure math perspective for that money to have never entered the pot, because he lost money by having to make that call. He is simple willing to make the call because the previous money in the pot is enough to make it worthwhile.

So in these situations, the player with the huge equity advantage should bet for value, even though the player on the draw is getting the proper pot odds to call. Every time more money goes into the pot, you should be happy in this situation.

ajmargarine
09-13-2005, 03:42 PM
I was actually trying to do an offshoot of a thread over in SSNL. My post here turns out to be silly as you should bet the \$20 every time. Even though it is correct for villian to call, you are still getting value from your \$20 bet. Basically the \$100 pot is static and doesn't really matter, and you should get an 80% return on that \$20.

Let me reask the question in the way it was intended.

--------------

Hero has A /images/graemlins/heart.gif A /images/graemlins/diamond.gif . We have a flop of 9 /images/graemlins/club.gif 6 /images/graemlins/club.gif 2 /images/graemlins/spade.gif . The pot is \$50 and hero and villain both have only \$25 left.

Villain is first to act, flips over his cards to show A /images/graemlins/club.gif K /images/graemlins/club.gif and checks to hero. Villain understands pot odds and won't call without them.

What should hero do?

Luzion
09-13-2005, 04:10 PM
[ QUOTE ]
I was actually trying to do an offshoot of a thread over in SSNL. My post here turns out to be silly as you should bet the \$20 every time. Even though it is correct for villian to call, you are still getting value from your \$20 bet. Basically the \$100 pot is static and doesn't really matter, and you should get an 80% return on that \$20.

Let me reask the question in the way it was intended.

--------------

Hero has A /images/graemlins/heart.gif A /images/graemlins/diamond.gif . We have a flop of 9 /images/graemlins/club.gif 6 /images/graemlins/club.gif 2 /images/graemlins/spade.gif . The pot is \$50 and hero and villain both have only \$25 left.

Villain is first to act, flips over his cards to show A /images/graemlins/club.gif K /images/graemlins/club.gif and checks to hero. Villain understands pot odds and won't call without them.

What should hero do?

[/ QUOTE ]

I think I know what you are asking. Obviously you are wondering if its better the push on the flop, or wait till the turn for a safe card and then put the max possible.

Alright, lets make some basic assumptations before we proceed. Lets assume he only has 9 outs. We will not be counting any runner runner Kings here. The probability he will make the flush from the flop to the river is 35% (2:1). The probability he will make the flush from the turn to the river is 19.5% (4.1:1).

There are really only 3 options that I can see.

1) Push your \$25 on the flop. He will call.
2) Check. The turn comes up blank. Bet as much as possible on the turn that he will call with. I believe this is \$12. \$50 + \$16 = \$66. He needs to put in \$16 to call, which gives him 4.125:1. Thats close enough.
3) Bet a small amount on the flop. If the turn is safe, bet the most possible.

For #1
0.35 * -\$25 = -\$8.75
0.65 * \$75 = +\$48.75

EV = \$40

For #2
(38/47)(37/46) * \$66 = \$42.92
(38/47)(9/46) * -\$16 = -\$2.53

EV = \$40.39

For #3 - Optimal way to get all his money in by the turn seems to be by betting \$6 on the flop, thus making the pot \$62. Then on a safe turn, betting all of your \$19, making the pot \$81, and giving him 4.26:1 to call with his remaining \$19.

(9/47) * -\$6 = -\$1.15
(38/47)(9/46) * -\$25 = -\$3.95
(38/47)(37/46) * \$75 = \$48.77

EV = \$43.67

Thus you can conclude, it seems best to bet a little on the flop, and then the rest of your money on the turn if it comes up blank.

AaronBrown
09-13-2005, 05:08 PM
I see your logic, but it has to be right for one of you to bet. Here's how I analyze it.

Out of 990 possible turn and river combinations, 630 win for you and 360 win for him. Since he has more than 1 chance in 3 of winning, he'll call any bet you make. If you bet \$25, your expected value is \$38.64. If he does fold, you get \$50 and are even happier.

If you check and he checks then either he gets a club or he doesn't. If he does get one, he's sure to win. You fold and end up with zero. If he doesn't, his maximum chance of winning is 25% (if he gets a King) so if you bet \$25, he folds and you get \$50. With an 80% chance of getting a non-club, this has an expected value of \$40 to you.

Therefore, you would prefer to check. But he can do the same math and will bet \$25, even though he has less than a 50% chance of winning.

09-13-2005, 07:35 PM
[ QUOTE ]
I see your logic, but it has to be right for one of you to bet.

[/ QUOTE ]

You're both right.
There are actually a couple of interesting turn cards:
A /images/graemlins/spade.gif gives the hero a set, and cuts off one of the villain's outs (2 /images/graemlins/club.gif is a boat)
K gives the villain a pair, and 2 extra outs for the set.
Any /images/graemlins/club.gif sends the hero to the bottom.

The trick here is that the implied odds are effectively worse than the pot equity.

The correct play for you is to bet \$5, and call any re-raise. The villain *should* go all-in, but you don't have to make that descision easy for him.

You have him trapped on the turn anyway on pot odds, so you can take the look for cheap; get out of dodge if it's a club and go all-in if it's not.

If you're splitting hairs, A/images/graemlins/spade.gif can come up on the turn and eat one of the outs, cutting his equity from .205 to .187 or so. So, in that situation, you should only raise \$18 on the turn so that he calls on pot odds.

Macquarie
09-13-2005, 08:11 PM
[ QUOTE ]
[ QUOTE ]
I see your logic, but it has to be right for one of you to bet.

[/ QUOTE ]

You're both right.
There are actually a couple of interesting turn cards:
A /images/graemlins/spade.gif gives the hero a set, and cuts off one of the villain's outs (2 /images/graemlins/club.gif is a boat)
K gives the villain a pair, and 2 extra outs for the set.
Any /images/graemlins/club.gif sends the hero to the bottom.

The trick here is that the implied odds are effectively worse than the pot equity.

The correct play for you is to bet \$5, and call any re-raise. The villain *should* go all-in, but you don't have to make that descision easy for him.

You have him trapped on the turn anyway on pot odds, so you can take the look for cheap; get out of dodge if it's a club and go all-in if it's not.

If you're splitting hairs, A/images/graemlins/spade.gif can come up on the turn and eat one of the outs, cutting his equity from .205 to .187 or so. So, in that situation, you should only raise \$18 on the turn so that he calls on pot odds.

[/ QUOTE ]

Nice post. We want to bet 5, but villain should come over the top of us.

In fact, villain should never have checked to us in the first place - he ought to have pushed himself.

Mr. Curious
09-13-2005, 08:21 PM
[ QUOTE ]
Any /images/graemlins/club.gif sends the hero to the bottom.

[/ QUOTE ]

You mentioned it before, but in a different way. If the 2/images/graemlins/club.gif comes on the turn, then Hero has 3 outs (2 hearts + 1 ace) to a boat that will win. So at that point, the equation flips and Villian must figure out the correct amount to bet so as not to give hero odds to win.

btw - I'm not clear why Villian should push the flop rather than checking. Villian may be only a 2:1 dog, but Hero would be getting 3:1 pot odds on a hand where he is a 2:1 favorite.

Macquarie
09-13-2005, 11:08 PM
Shouldn't villain push rather than check, to prevent hero from taking the option to check behind?

If hero bets small, villain should come over the top. Hero's best option is therefore to check behind. Villain should push himself in order to prevent hero taking his best option.

Doesn't forcing hero into his lowest EV option equate to villain getting the best EV?

09-14-2005, 11:00 AM
[ QUOTE ]
[ QUOTE ]
Any /images/graemlins/club.gif sends the hero to the bottom.

[/ QUOTE ]

You mentioned it before, but in a different way. If the 2/images/graemlins/club.gif comes on the turn, then Hero has 3 outs (2 hearts + 1 ace) to a boat that will win. So at that point, the equation flips and Villian must figure out the correct amount to bet so as not to give hero odds to win.

[/ QUOTE ]

The thing is that, on a \$60 pot even with the 2/images/graemlins/club.gif on the turn, the villain has enough money to push the hero out of the pot (\$20). Since both players know pot odds, that means that the villain has no +EV moves if a 2/images/graemlins/club.gif comes up. (In this scenario, the villain bets \$5.56,and the hero calls or folds.)

[ QUOTE ]

btw - I'm not clear why Villian should push the flop rather than checking. Villian may be only a 2:1 dog, but Hero would be getting 3:1 pot odds on a hand where he is a 2:1 favorite.

[/ QUOTE ]

It comes down to the fact that the hero won't be calling into a flush, and, if the turn is not a flush, then the hero can get money into the pot at better odds.

Alternatively, you can think of it as:
All-in the pot odds are 363/990
Otherwise the pot odds are 9/45=198/990

Also, as a known underdog, the villain gets 3:1 pot odds on his raise since the hero will be calling. Now, 9/45*50=10 is the (naive) net value of checking, and 363/990*100-25=11.4 is the net value of going all in. Therefore going all in is better than checking.

(This is a slight simplification, since, at bets of more than \$5, the villain is trapped, and must call up to all-in on the turn.)

09-14-2005, 11:10 AM
[ QUOTE ]
Shouldn't villain push rather than check, to prevent hero from taking the option to check behind?

If hero bets small, villain should come over the top. Hero's best option is therefore to check behind. Villain should push himself in order to prevent hero taking his best option.

Doesn't forcing hero into his lowest EV option equate to villain getting the best EV?

[/ QUOTE ]

You understand the math of the situation completely.

However, the villain has already checked - so I assumed that he is not aware that his best move is to go all in. Thus, since he's an underdog, but has pot odds we can reasonably expect him to call with the implied odds, this means that the \$5 buys the hero \$8 worth of pot for a profit of \$3.

With a probabilistic opponent, the hero should raise \$5 if the villain goes all in less than about 2/3 of the time since all in is a net loss of about \$1.4

bizaff
09-15-2005, 02:56 PM
I'm coming from the SSNL thread too, and I'm struggling with coming up with the math for the flop and turn bets from the perspective of the flop.

This (http://forumserver.twoplustwo.com/showflat.php?Cat=&amp;Board=ssplnlpoker&amp;Number=3395887 &amp;Forum=f25&amp;Words=&amp;Searchpage=0&amp;Limit=25&amp;Main=33887 96&amp;Search=true&amp;where=bodysub&amp;Name=30353&amp;daterange= 1&amp;newerval=1&amp;newertype=w&amp;olderval=&amp;oldertype=&amp;body prev=#Post3395887) is my analysis of the original question addressing a flop push vs a flop check and safe turn push. How do I adjust the math to take a flop bet into account?

09-16-2005, 01:54 AM
This got in my head, and it seems like there's a more fun example:

Let's say you come into this situation with
Hero's hand: Q/images/graemlins/diamond.gif J/images/graemlins/diamond.gif
Villain's Hand: A/images/graemlins/club.gif A/images/graemlins/heart.gif
Board: J/images/graemlins/heart.gif T/images/graemlins/diamond.gif 9/images/graemlins/diamond.gif

So, the fun cards are:
9 diamonds for the flush
6 Kings or 8's for the straight
3 Queens for 2 pair
2 Jacks for the set

So there are (essentially) 20 outs - the straight/flush draw wins 640 and the aces get 341.

Let's say that the pot is 1,000 chips, and that hero and villain have 1,000,000 chips each, and the hero is under the gun, what is the hero's correct action?

Alternatively, if the villain acts first, what is the villain's correct action?

Mr. Curious
09-16-2005, 01:38 PM
Hero is the favorite, so Hero would be happy to push and have Villian call, even though Villian is ahead at the time.

Hero can call any amount that Villian bets (including an all-in) because on the flop, Hero is a 60%+ favorite at that time.

09-16-2005, 04:20 PM
[ QUOTE ]
Hero is the favorite, so Hero would be happy to push and have Villian call, even though Villian is ahead at the time.

Hero can call any amount that Villian bets (including an all-in) because on the flop, Hero is a 60%+ favorite at that time.

[/ QUOTE ]

I'm not sure of what you mean by push, but the hero should go all-in. Anything less leaves money on the table.

The villain should call any bet up to roughly 55,000, and the hero *must* re-raise to all-in. Calling smaller bets is a losing proposition here.