Giving Free Cards

[Pelion]

Ok first off it think its pretty obvious that if you are going to be called anyway then you may as well wait a card to see if you are beaten before you bet. This is what counterplay is based on and its a strategy that works. First let me say that this is an extreme example but it is ment to illustrate a concept that could apply to less extreme situations.


The Maths

Situation:
All of the cards are face up.

Hero Holds: A K
Villain Holds: 7 8

Flop: K 5 6 || Pot Size $320

Villain has 9 diamond outs and 6 more straight outs for a total of 15 outs.

You have excactly 1/4 of the pot remaining in your stack so how ever you play it he is correct to call (getting 5:1).

Method 1

You could push allin as you don't want to give a free card.

Villain calls as he is getting the correct pot odds. We will assume the only way villain can win is by hitting the flush or straight. ( He also has runner runner outs but we ignore these as they dont affect the calculation much).

Chance of NOT making the flush on the turn

There are 15 cards left that complete the draw so there are 47-15 = 32 cards left that do not.
n or river.

chance of NOT making the flush on turn or river is:

32/47 * 32/46 = 512/1081


So the chance of the straight or flush coming is: 569/1081

So in 1081 trials,
569 times Hero loses $80. EV =( 569*-80)/1081 = - 42.109
512 times Hero wins $400. EV = (512*400)/1081 = 189.454

Total EV = 189.454 - 42.109 = 147.345


Method 2:

Hero checks flop then is allin on a non straight/flush turn. Hero folds if turn completes the draw.

In 2162 trials,
15/47= 690 times Hero folds the turn and wins 0. EV = 0
32/47 times hero is allin on the turn.

Of those 32 times:

15/46 = 480 times Hero loses $80. EV = -17.761
31/46 = 992 times Hero wins $400. EV = 183.534

Total EV = 183.534 - 17.761 = 165.773

So if your opponent will call you anyway whether you push the flop, or turn it is better to take a free card and make sure it isnt one of your opponents outs before you push. On this occasion he is making a mistake by GIVING YOU a free card as it is a free chance to get away from the hand.. The best way to think of it is that you have outs to the winning hand, but that your outs are all of the blanks.

Obviously this only applies completely when you are VERY short stacked and when you KNOW what your opponents cards are but it is something to be considered if you think your opponent has a lot of draws.

I originally wrote this as a sort of answer to a Hand History post where it doesnt quite apply because its a little hypothetical so il put it here and see what you guys make of it.

[Telepath]

This is of course right. Problem is how to find a situation where this is ever truly applicable.

Poker isn't a game of open cards.

T.

[Pelion]

It is applicable in any situation where you feel your opponent may be pot commited. You just have to think real hard first about why you think they are pot commited and what cards you are trying to avoid.