EV quiz (NLCASH)

[roommate]

[ QUOTE ]
preflop?

[/ QUOTE ]

I did my analysis preflop... but after rereading the question... I guess the original poster intended the question to be answered on the river.

OP, not enough information to provide a correct answer... could you tell us the board? and stack sizes? and flop/turn action?

ty~
~rob

[acidca]

52.65:47.35 are the exact odds.

[roommate]

good call acidca... but i was doing that off the top of my head. I bet you used a calculator.

~rob

[martial]

Hey acidca the odds are 52.65:47.35,but is the AK correct to call if you give him the right price acording to this odds ,but it is very close to it.
Asuming we have very big stacks he will not flop hand that is favorit to win 47.35 and he will have to fold it on the flop.
Stack sizes matter,so if we have unlimited stacks and can bet any ammount postflop,the question is what are the odds AK will flop hand that is favorit.

[jay_shark]

I realized I never answered my own question .

Lets ignore ties and say that 2c 2d is a 52.26% favourite . (according to pokerstove) . This means AcKd will win 47.74% .

Let x be the amount to bet . If you bet x (after you post blinds) , then villain is receiving (x+3)x-1) pot odds .Solve for x when (x+3)x-1) = (100-47.74)/47.74
(x+3)/(x-1)= 1.0946
x=43.28

This means that if hero bets more than 43.28 , then it will be incorrect for villain to call .

[aaaaa]

Before solving your problem, let me look at a much simpler problem first. PLEASE note the probabilites are from memory but the approach remains the same.

I am assuming he is a calling station, which is a reasonable assumption for this hand and game.

1. SIMPLIFIED PROBLEM --
He has missed turn and flop. Only river remains to be seen.
Let Z be pot size post-turn. And r be my bet size before we see the river.

The prob of winning on river = 12%, odds = 7:1
So (Z+r)/r = 7:1, so r = Z/6 .........(1)
What is the EV of this game then? It is 0.

2. SLIGHTLY MORE COMPLICATED --
He has missed flop. Turn and river remain to be seen.
Let Y be pot size post-flop. And t be my bet size before we see the turn.

The prob of winning on turn = 12%, odds = 7:1
So (Y+t)/t = 7:1, so t = Y/6 .........(2)

Why have we not included the IMPLIED ODDS here? Because the EV of continuing on the river for our villian is 0 by equation (1) above and *he knows that*. (Alternatively we may include the implied odds, if we want to be extra careful.)

So anyway, what is the EV for this game? It is 0.... we have made it to be 0.

Jay do you agree with this? Only then I shall proceed to the next part of my attempt!

thanks

[jay_shark]

Well it's negative EV for villain only if hero doesn't spew EV on the flop .

If you assume that villain gets to see the turn and river for free (hero puts all his money pre-flop) then he cannot call more than 43 and change .

The EV for this particular situation is that hero wins back the blinds if both players are playing optimally .

[aaaaa]

I don't see why going all-in pre-flop is optimal as you mentioned.

EV = blinds .....(1)

Now suppose I break 43 = bet 26 on flop + bet 17 post-flop (I fold if he bets after flop)
Note that this is acceptable to villain as after flop, the pot is 52 (+ blinds) and he requires 3:1 odds (to the river) which he gets with calling 17.

Let's ignore the blinds, the effect is pretty small.

So we have three cases --
1. villain hits on flop: prob = .5, payoff to hero = -26
2. no hit on flop, hit on turn/river: prob = .5* 1/4, payoff to hero = -43
3. no hit on flop, hit on turn/river: prob = .5* 3/4, payoff to hero = 86

Summing up the EVs we get EV = 17 ........(2)

PLEASE COMMENT! My math/assumptions may be way off.

I am doing a binomial tree approach like it is done for options pricing. I am basically making EV = 0, at every stage in the game for the villain. And for that I have to start backwards (as it is independant of previous streets).

thanks

[aaaaa]

In the above case the probabilities are:
hits on flop: 1/3
does not hit on flop, but hits on river/turn: 2/3*1/4
does not hit on flop, does not hit on river/turn: 2/3*3/4 (= 1/2 as expected)

So the EV's are -26*p1 + -43*p2 + 86*p3
=27

[jay_shark]

Please make a new thread so we can discuss this in more detail without hijacking this one .

The situation I described is when you know your opponents hole cards and that all of your money is going in pre-flop .