Poker math quiz: evaluate this hand.

[bozzer]

I'm going to give us 5 outs on the flop, to represent the chance he has better than a pair. 5 outs*2 = 10%

i'm assuming if we make a pair of kings or better we stack him.

i'm assuming we check the turn and we check back if we can.

i'm assuming we are behind.

i am assuming we don't usually have odds to call if he shoves turn.

our equity on the flop call is:

equity if we only see turn + implied equity + equity if we see river for free * chance we see the river for free = EV on the call.

equity if we only see turn: 0.1($39.50) - $7 = -$3.05

implied equity: 0.11*$11 = +$1.1

equity if we see the river for free = 0.1($39.5) = +$3.95

chance we see the river for free = ???

solving at EV = 0 to find the chance we see the river for free (x) to have a breakeven call:

-3.05 + 1.1 + x(3.95) = 0

1.95 = -x(3.95)

1.95/3.95 = -x = 0.49

i've messed up a - somewhere but don't sweat it.

we need him to check the turn >50% of the time to have a +EV call on the flop.

i vote that he checks turn less than a third of the time here.

edit: hmm i should probably have a chance we only see the turn = 1 - chance we see river term in there. that gives a different answer and makes a call more likely to be good. i wll correct later.