Figuring out when this will be +EV

[Schizo]

A fellow 2+2'er posted this in SS.

Party Poker 3/6 Hold'em (9 handed) converter (http://www.selachian.com/tools/bisonconverter/hhconverter.cgi)

Preflop: Hero is UTG with K/images/graemlins/diamond.gif, K/images/graemlins/club.gif.
<font color="#CC3333">Hero raises</font>, UTG+1 folds, MP1 calls, MP2 folds, MP3 folds, CO folds, Button folds, SB folds, BB folds.

Flop: (5.33 SB) 4/images/graemlins/spade.gif, 9/images/graemlins/spade.gif, 7/images/graemlins/club.gif <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, MP1 calls.

Turn: (3.66 BB) 3/images/graemlins/spade.gif <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, MP1 calls.

River: (5.66 BB) 7/images/graemlins/spade.gif <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, <font color="#CC3333">MP1 raises</font>, Hero folds.

Final Pot: 8.66 BB


My question is:

What is the probability that villian has a spade?
Taking into account the number of times villian has a spade, at what frequency (relative to the numer of times villian doesn't have a spade) does villian have to be bluff raising to make this call profitable?

[gaming_mouse]

There are 9 spades left, 45 cards left. Assuming a random hand for him (false, but ok for the purpose at hand), the chance that he does not have a spade is:

(36/45)*(35/44)=.63

63% I'm good. However, that is just our baseline probability. The important part of the story can't be quantified so readily:

1. Why is he calling down? Flush draw looks likely, especially after the turn.
2. What is the chance, given he does not have a spade, that he has correctly put me on a non-spade hand and thinks that I will fold to a raise. As the board must look scary to him too, this seems quite unlikely. Unlikely enough to justify my fold?

There are 7.66BB in the pot.

.63*(chance he's bluffing w/out a spade)=(1/8.66)
chance he's bluffing = .18

Unless you think the odds of your oppo bluff-raising here are better than 4.5:1, you should fold.

gm

[jokerthief]

[ QUOTE ]
There are 9 spades left, 45 cards left. Assuming a random hand for him (false, but ok for the purpose at hand), the chance that he does not have a spade is:

(36/45)*(35/44)=.63



[/ QUOTE ]

I understand that (36/45) means there are 9 spades and 45 unknown cards but am lost as to what the second event means. Could you explain that to me?

Thanks
jokerthief

[gaming_mouse]

[ QUOTE ]

I understand that (36/45) means there are 9 spades and 45 unknown cards but am lost as to what the second event means. Could you explain that to me?

Thanks
jokerthief

[/ QUOTE ]

We are calculating the chance of his not having a spade. First, there are 36 non-spades out of 45 cards left. After his first card is a non-spade, there are now only 35 non-spades left, and 44 cards left total

[jokerthief]

I really need to get to bed...duh!

Thanks for the help
jokerthief

[soko]

If you want to 'calculate' if your hand is good you can use this simple formula:

You = no spade
Board = 4 spades
opponent = raise
You = lose

[gaming_mouse]

[ QUOTE ]
You = no spade
Board = 4 spades
opponent = raise
You = lose

[/ QUOTE ]

Versus a tricky TAG, this is silly.

A very good player would have put me on a made pocket pair, which means, if he has balls, a bluff raise might be profitable for him (50% chance it works), especially if he knows that I keep betting with top pair no spade.

Having said that, I still think it's unlikely and that the fold was good, for reasons I've already stated.

But it is not a foregone conclusion, and thinking like this in higher limit games, against tricky, aggressive oppos will get you in trouble. As this was 3/6 and I had no reason to think he was THAT tricky, it's fine.

gm