Basic equity/pot odds math question

[dirtylobster]

A friend just asked me about this and I tried to think it through but I'm not sure if I have it right so please correct me where/if I'm wrong.

NL 0.5/1, $100 stacks.

Hero is dealt JJ UTG, opens for $4

folded to SB who raises to $12
BB folds

Is it profitable to 4-bet to $40 here?

The problem being.... let's say he only 3-bets premium hands (QQ/KK/AA/AK). Then it's obviously a mistake to 4-bet as it prices us in to call a shove (36% equity), right? But... if we assume his 3-betting range also includes JJ/TT/99/AQ. Now our equity is about 50%.

Let's assume he always folds the second range to a 4-bet and always shoves the first range.

10 times.

5 times he'll fold, giving us 5 x $17 ($1 blind + $4 open + $12 raise) = $85

5 times he'll shove and we're priced to call. 5 x our $100 to win 5 $200 pots w/ 36% equity.... 0.36 x $1000 gives us $360 right. So $500 invested, $360 won. That shows a negative profit of -$140.

Totally this gives us $85 - $140 = -$55 over 10 hands which would lead us to the fact that 4-betting is not profitable assuming this specific range.

Am I on the right track so far?

[dirtylobster]

No takers?

[PartysOver]

you have to do the number of combinations for each one,

a real easy way to do it is highlight them in stove and see what #'s pop up, so it's not 5/10 times it's...

total 3b range: 5.1%
premo 3b range: 2.6%

2.6%/5.1%=50.9% he shoves (in this case you're real close but for future)

so 50.9%(-$140)+49.1%(+$85)= ~ -$55

that's how you do it.

edit/i didnt take into account you had jj and there's only one combo left, so 5.1% should be 4.8% etc

[PartysOver]

also, to figure out how wide his 3b range must be to breakeven on a push... it's

X=% he pushes with QQ+, AK

X(EV if called)+(1-X)(pot)=0

so if he only pushes say 25% of his 3b range, you're likely +ev