Betting into a 4 flush.

[Nottom]

OK, you have black kings and the board is

Q /images/graemlins/heart.gif T /images/graemlins/heart.gif 7 /images/graemlins/spade.gif 4 /images/graemlins/heart.gif 2 /images/graemlins/heart.gif

You are playing terrible players and will be called by a pair or better and only raised by a flush.

How many opponents must you have before this bet is -EV?

(Make whatever assumptions you want, but state them for us if you do.)

[thirddan]

OOP i would bet into one player that has just been calling all the way, but would check it against two...

In position i would probably just check it through, or bet against one really loose/passive player...

[soko]

Your missing the key element to this scenario... how big is the pot?

[K C]

It's true that the size of the pot is kinda important /images/graemlins/smile.gif However, let's look at this in terms of your chances to win first. We'll assume that they will need to flush to beat you. Now, there's 9 hearts out there, and every player has 2 cards of course. And if anyone has a heart, you're screwed. Out of 45 cards, there's 1 chance in 2.5 that an opponent has made the flush. So with 1 opponent it's going to be easy. You're a 60% fav to win. With 2, you only have a 20% chance, so it gets more dicey. Chances are the pot will give you odds to call, but you must look at the players' moves as well. For instance, if you know the players would only raise when he has you beat, and there's an 80% chance of this happening, you've got to lay it down.

KC
kingcobrapoker.com

[CaptLego]

[ QUOTE ]
It's true that the size of the pot is kinda important /images/graemlins/smile.gif However, let's look at this in terms of your chances to win first. We'll assume that they will need to flush to beat you. Now, there's 9 hearts out there, and every player has 2 cards of course. And if anyone has a heart, you're screwed. Out of 45 cards, there's 1 chance in 2.5 that an opponent has made the flush. So with 1 opponent it's going to be easy. You're a 60% fav to win. With 2, you only have a 20% chance, so it gets more dicey. Chances are the pot will give you odds to call, but you must look at the players' moves as well. For instance, if you know the players would only raise when he has you beat, and there's an 80% chance of this happening, you've got to lay it down.

KC
kingcobrapoker.com

[/ QUOTE ]

If the hand started with 8 or 10 people, then I'd think that with two remaining at the river that the chances they have hearts is much greater than random. The people without hearts would be more inclined to fold earlier, and those with a heart or two would be more inclined to stick around..

[maurile]

[ QUOTE ]
Your missing the key element to this scenario... how big is the pot?

[/ QUOTE ]
The size of the pot doesn't matter at all. It's already been stipulated that a better hand than yours isn't going to fold, and a worse hand isn't going to bluff-raise.

[pif]

if u play against 3 ur odds to win = 14% (chance they have best hand: 8% 2pairs, 1% 3kind, 76% flush)

against 2 chance to win= 28% (9% 2pairs, 2% 3kind ,60% flush)

against 1 chance to win=55% (7% for 2pairs, 1% for 3kind, 36% flush)

hope i helpd u

[CaptLego]

[ QUOTE ]
[ QUOTE ]
Your missing the key element to this scenario... how big is the pot?

[/ QUOTE ]
The size of the pot doesn't matter at all. It's already been stipulated that a better hand than yours isn't going to fold, and a worse hand isn't going to bluff-raise.

[/ QUOTE ]
I think the size of the pot does matter. It also matters how many people saw the flop and the turn.
For example, if 8 opponents saw the flop and they are terrible players, then anybody with a heart might decide to go for the backdoor flush draw. If 4 people see the turn, then anybody with a heart is getting pot odds to see the river (especially if the pot is large). So when you calculate the odds of anybody having a heart, you may need to use the # of people that saw the turn, rather than the # of people that saw the river.

[K C]

You're right to point out that this might not exactly be random, but in a lot of cases it will be. There's going to be some instances where players will draw to this flush, but it's pretty much only going to be when they have a fairly high card in the suit. And this player is already being accounted for. That's not going to be the case more often than not, so in most cases we can go ahead and use random hands. Keep in mind that the exercise here is to determine what number of opponents in the hand would cause you to be in trouble, and we don't need to go beyond random hands to determine that two is the number. And against a single opponent we're going to have the advantage regardless with our hand.

As far as how much being in the pot not mattering, every poker decision we make must take into account how much is in the pot. In this case, we determine what our probability of winning the hand is, take how much it will cost us to play on, and how much we stand to gain if we win. There is no other way to approach this, and it necessitates considering and applying pot size.

KC
kingcobrapoker.com

[LinusKS]

Against one opponent you should never make this bet.

There are only three possibilities:

1. Your opponent will fold, gaining you nothing.

2. Your opponent will call, gaining you one bet.

3. Your opponent will raise, costing you two bets.

The chance that a random hand contains a heart is 36%.

That means 36% of the time you'll be raised, so you'll lose 72 bets out of every hundred times you do this. Even if your opponent always called every time you beat him, nd you beat him every time he called, you only collect 64 bets the other 64/100 times. The net result is minus 8 bets per 100.

Of course, the actual results will be worse, since he won't always call, and you won't always win when he does. So in reality the bet is much worse than that.

I haven't done the math for multiple opponents, but it seems like that situation must be worse, since the math quickly becomes overwhelming. If you have even two opponents, the chances at least one of them has a heart should be somewhere around 70%, so you lose two bets 70% of the time, and win two bets (or less) 30%.

In this situation, the size of the pot is irrelevant.

[ QUOTE ]
OK, you have black kings and the board is

Q /images/graemlins/heart.gif T /images/graemlins/heart.gif 7 /images/graemlins/spade.gif 4 /images/graemlins/heart.gif 2 /images/graemlins/heart.gif

You are playing terrible players and will be called by a pair or better and only raised by a flush.

How many opponents must you have before this bet is -EV?

(Make whatever assumptions you want, but state them for us if you do.)

[/ QUOTE ]

[maurile]

[ QUOTE ]
As far as how much being in the pot not mattering, every poker decision we make must take into account how much is in the pot. In this case, we determine what our probability of winning the hand is, take how much it will cost us to play on, and how much we stand to gain if we win.

[/ QUOTE ]
That's fine for determining whether or not to fold to a bet . . . but we're not facing a bet here. It's also fine for determining whether or not to bluff at a pot . . . but it's been stipulated that bluffing here is useless. It's normally fine as well for determining whether to value-bet the river since the size of the pot is normally a factor affecting what range of hands your opponent will call with. But in this problem, it's already been stipulated that they'll call with any pair regardless of the size of the pot.

So the size of the pot doesn't matter a lick.

(If you think the size of the pot does matter, go ahead and give two different answers: one for a pot of zero, and one for a pot of a million big bets. And explain why the answers are different.)

[maurile]

[ QUOTE ]
OK, you have black kings and the board is

Q /images/graemlins/heart.gif T /images/graemlins/heart.gif 7 /images/graemlins/spade.gif 4 /images/graemlins/heart.gif 2 /images/graemlins/heart.gif

You are playing terrible players and will be called by a pair or better and only raised by a flush.

How many opponents must you have before this bet is -EV?

(Make whatever assumptions you want, but state them for us if you do.)

[/ QUOTE ]
Against a single player, it is +EV if he has something between a pair of twos or a pair of queens, inclusive. It is EV-neutral if he has worse than a pair of twos, and -EV if he has better than a pair of queens. (He can't tie you, because if he also has KK, he's got the flush.)

Against a single opponent, there's a 16.5% chance he has exactly one pair lower than kings. (There are 18 combination of heart-less pocket pairs: three ways each to get 3s, 5s, 6s, 8s, 9s, or Js. And there are 66 ways each of getting a heart-less pair of Qs, Ts, 4s, and 2s. There are 44 ways to get a heartless pair of 7s. That's 326 ways of losing to KK with a pair, out of 45*44 = 1980 possible hands. 320/1980 = 16.5%.)

There is a 45.9% chance of losing to a random hand with black kings given the specified board, according to PokerStove.

So betting into even a single opponent is -EV since 45.9% > 16.5%:

45.9% of the time you bet, you will be called (or raised) and lose.

16.5% of the time, you will be called and win.

37.6% of the time, you will not be called.

[maurile]

I should have read LinusKS's post before making mine. I agree with his conclusion, although I think we can fold to any raise, so we're still just losing 36 bets when our opponent has a flush (and another ten bets when our opponent has two pair, a set, or a pair of aces).

But the bet is still -EV even given that we can correctly fold to a raise, as long as our opponent won't call without at least a pair.

[Cheeseweasel]

This won't precisely answer your question but perhaps it will help.

Hero = KcKs
Board = QhTh7s4h2h

"Loose" Table:

(1) Hero
(1) "Solid"
(4) "Typical"
(3) "Fish"
(1) "Maniac"

Hero EV = -1.1BB/Hand
Hero Win_% = 28.6

Best of Luck

[LinusKS]

[ QUOTE ]
I should have read LinusKS's post before making mine. I agree with his conclusion, although I think we can fold to any raise, so we're still just losing 36 bets when our opponent has a flush (and another ten bets when our opponent has two pair, a set, or a pair of aces).

But the bet is still -EV even given that we can correctly fold to a raise, as long as our opponent won't call without at least a pair.

[/ QUOTE ]

Your answer is better. I hadn't considered that you could fold to a raise, which considering the stipulations, you obviously could.

[SeattleJake]

This was the best response yet. Are you using PokerStove to arrive at these, or something else?

[SeattleJake]

Also, this does show that pot size matters. If you only had a 14% chance of winning, but the pot size is 6bb, then it's still +ev.

[maurile]

[ QUOTE ]
Also, this does show that pot size matters. If you only had a 14% chance of winning, but the pot size is 6bb, then it's still +ev.

[/ QUOTE ]
When you say "it's still +ev," what is the "it" you're referring to?

If "it" means betting, you are wrong. Pot size doesn't matter since betting doesn't increase your chance of winning the pot.

(Once you've decided not to bet, your choice is between check-calling and check-folding. That does depend on the size of the pot, as long as your opponent will sometimes bet with hands you can beat.)