Raising vs. checking a small pocket pair in the BB vs large field

[VBM]

This question came up in reg.gambling.poker, and I laughed at the way the respondents reasoned why you should't raise 44, 55, 66 in BB.

I also believed checking was better (not for the reasons they stated, check out the microlimits post if you're interested) but now I'm having some 2nd thoughts...?!

(disclaimer, i was, at best, a mediocre/dispassionate math student, so please laugh behind my back after i leave the forum? /images/graemlins/smile.gif)

Scenario:
Limit Hold'em, dealt 44, 55, 66 in BB.
7 limpers.

Check or raise? I figured checking is the best move but I tried to work out the EV decisions...

assumptions:
1. if you make your set off the flop, you will win.
2. if you raise, everyone will call, no one fold or raise.
3. for simplicity's sake, lets say it's a 1-dollar bet.


EV of raising:
EV of a raise = (.12) * 16 + (.87) * -1 = 1.92 - .87 = 1.05

EV of checking
EV of a check = (.12) * 8 + (0.87) * 0 = 0.96

I realize this poker decision cannot be made without consideration for the opponents and greater implied odds should you make your set (not to mention your abyssmal position if you do) and also the assumptions are very broad, but am i crazy in thinking, a raise, purely working in this framework, isn't bad?

[Lost Wages]

[ QUOTE ]
EV of a raise = (.12) * <font color="red">16</font> + (.87) * -1 = 1.92 - .87 = 1.05


[/ QUOTE ]

The 16 should be a 15. You can't win your raise. In other words, when you win you will have 15 more units than you started the hand with (after posting). In addition, your percentages are rounded off a bit. You will flop a set/full house or quads 11.76% of the time.

EV(raising) = (.1176)*(15) + (.8824)*(-1) = .8816
EV(checking) = (.1176)*(8) = .9408

Lost Wages

[VBM]

thanks Lost...can you also help me out w/ the 11.76%?

my assumption was; 2 cards out of 50 unseen X 3 would be 6/50 hence 12/100 = 12%?

[Pokerscott]

Let's see 2 cards to hit with 50 unknown.

Prob not hitting = Prob doesn't hit with card 1 and prob doesn't hit with card 2 and prob doesn't hit with card 3

= 48/50 * 47/49 * 46/48

= 88.24%

Prob hitting = 1 - prob not hitting

= 11.76%

Since the number of outs is so low you can approximate this with 2 (outs) * 3 cards to show / 50 cards unknown = 6/50 = 12%

pokerscott

[VBM]

ah...perfect. thank you!