probability he has a Ax if . . .

[whaahhahahah]

-he calls 30% total
-he calls 100%
-he doesn't reraise
-an ace flops
-i don't have an ace

Here's my attempt:

1. p(Ax if i have no A and he calls 100%) = 100 - (46/50 x 45/49) = 16%

2. p(Ax if i have no A and he calls 100% pf and the flop is Axx) = 100 - (44/47 x 43/46) = 12%

3. p(Ax if i have no A and he calls 30% total) = 100(16/30) = 53%

(should i have used bayes for 3?)

4. p(Axx flop if i have no A and he has Ax) = (3/48 x 45/47 x 44/46) x 3 = 16%

5. p(Axx flop if i have no A and he has no A) = p(4/48 x 44/47 x 43/46) x 3 = 22%

so i'm using bayes to try to tie this up --


p (Ax given i have no A, he calls 30% total, he calls all Ax, the flop is Axx) =

p (Axx flop given Ax) x p(Ax if i have no A and he calls 30% total)/p(Ax if i have no A) =

(.16)(.53)/(.16) =

53%

Is this a fluke? Does this make sense?