Game Theory

[doubleup]

In answer to your original question.

The number of times you bluff purely depends on the bet size you make. If you bet half the pot then for every two times you bet with the flush, you should bluff once. To achieve this you should decide before the river card which heart cards you will bet on (i.e 2-8 hearts) and which you won't (i.e. 9-A of hearts). In this situation you should bet on any heart because you are going to pot the river.

However, you should be able to get a higher EV than this by accurately gauging your oppo's and figuring out which ones are more likely to call pot sized river bets and which ones won't.

If you want to get really complicated you could look at building the pot on the turn to setup your river bluff.


Edit: actually i made a mistake. When you bet half of the pot you should bet on 4.5 hearts and when you pot it you should bet on 9 hearts.

Hmmm Not sure this is maxing profitability

lets say the pot is 2 units on the turn and 4 on the river.

You are proposing that we fold 7 of 10, bluff 1/10 and bet 2/10

If he calls  half pot all the time then we lose 7 misses, lose 3 for one called bluff, and win 10 for the calls when we are good - still break even

[matt674]

hehehe i love it when people get into these deep and meaningful mathematical discussions...........

Then they sit down at their computer to play an online game and within 5 seconds the screen is beeping "its your turn - you have 10 seconds or you hand is folded".

Lol, plenty of time to get the monkey abacus out and start calculating pythagorus

[thetank]

Might be easier to put some numbers to it.

[thetank]

hehehe i love it when people get into these deep and meaningful mathematical discussions...........

Then they sit down at their computer to play an online game and within 5 seconds the screen is beeping "its your turn - you have 10 seconds or you hand is folded".

Lol, plenty of time to get the monkey abacus out and start calculating pythagorus

The more you run dry theory, the better your instinct gets, the luckier you become.

[doubleup]

Might be easier to put some numbers to it.

You bluff the pot half the time the other flush lands and doesn't pair the board I think

Lets say the pot is 4 units after he bets the turn and you call.

Out of 10 goes:

So If he folds all the time

You lose 7 units when you don't bet.

You win 9 units the 3 times you bet.

9 minus 7 = 2

So if he calls all the time:

You lose 7 units when you dont bet

You lose 5 units when you bluff and are called

You win 14 units the 2 times you are called and are good.

14 minus (7+5) = 2

So if you bet the pot 50% of the time the other flush hits you are guaranteed a profit of the pot on the flop - thats quite a lot I think.

[thetank]

Nope, no easier. 

[SupaMonkey]

I had all of this stuff figured out once, but now i can't seem to remember it. Give me a minute.

[SupaMonkey]

Ok, i remembered it wrong, sry 

If you bet half the pot you should bluff 1-3 (or 1/4) times, not the 1-2 i said above (oops).

If he calls everytime, you win 1.5 everytime you have it (the pot plus the half he puts in) = 3 times, and you lose 0.5 the one time he catches you bluffing.
This equals +4.

If he folds you win the pot each time = +4




Likewise, if you pot it you should have a bluffing ratio of 1 in 3 (because when he calls (this is the bit i forgot) you will have put 1 unit into a pot of 3).

He calls everytime,
You win 2 twice and lose 1 once = +3

He folds everytime,
You win 1 each time = +3

Hope this makes sense, sry for the earlier mistakes.

[SupaMonkey]

So in answer to your above question you pot it on 4.5 of the remaining hearts.

[doubleup]

So in answer to your above question you pot it on 4.5 of the remaining hearts.

Which is the same as

"You bluff the pot half the time the other flush lands and doesn't pair the board"


Anyway now that we've estabished what we're talking about - how do we get into situations where this can be used?

[SupaMonkey]

You should be able to beat optimum bluffing returns by picking your spots and it really has it's place in games where you can't see the last card, like stud (and also for randomising your plays). Personally, after i understood it i didn't really look at it further. In the situation you described above, wouldn't you just be thinking, would this guy fold to a pot bet here.

[M3boy]

Re Raise him on the turn, you then can bluff the river whatever card comes out!