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Marginally negative, thus check. Play with the assumptions if you think they should be different.

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You could also work with weighted combos, but I think your % are close. I do think A[img]/images/graemlins/spade.gif[/img]K[img]/images/graemlins/spade.gif[/img] could be weighted a lot more after the river check.

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Anyway, say BB has AA or KK 50% of the time, JJ or TT 40% of the time and AK 10% of the time. SB has a random PP or paired the board 75% of the time and hit is crummy straight 25% of the time. BB will call any PP but not AK. What's out EV?

BB wins 50% * -1 = -0.5
SB wins 25%*50% * -1 = -0.125
We win, BB and SB call 40%*75%*2= +0.6
We win, BB folds, SB calls 10%*75%*1= +0.00075

Total EV = -0.02425


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This math needs correcting. Those % are additive so:

BB Wins= -0.5
SB Wins= 0.25
These two can combine into 1 calc:
SB Wins or BB wins= 25%(-1) + 50%(-1) = -0.25 + -0.50 = -0.75

We win, BB and SB call 40%(1)+75%(1)= 1.15
We win, BB folds, SB calls 10%(0)+75(1)=0.75

Total EV = 1.15

There are also the chances SB or BB c/r and we fold(or call - that pot is huge) after betting
or chance that neither call. But, probably don’t affect the EV too much.