Hi

It's fairly simple actually and la55i has it almost spot on although you should have 43/44 as the second term, not 44/45. Remember there's one less card in the deck OTR. The difference is so small that the result will be almost the same, but still it's not 100% correct

To maybe make it a bit more visual...

There's basically 5 things that can happen, 2 of which result in villain winning:

a. Villain doesn't hit

b. Villain hits turn, you miss river

c. Villain hits turn, you hit river

d. Villain misses turn, hits river where turn is a 3

e. Villain misses turn, hits river where turn is not a 3

**code:** | a = 41/45 * 40/44 = 82.83%
b = 4/45 * 43/44 = 8.69%
c = 4/45 * 1/44 = 0.2%
d = 1/45 * 4/44 = 0.2%
e = 40/45 * 4/44 = 8.08% | |

(a, c and d aren't strictly necessary for the calculation, but added them just to make it a bit more clear)

So villain's equity here is basically b + e which is 16.77%.

So if you would put that in one equation, you would get:

**code:** | Villain's equity = 4/45 * 43/44 + 40/45 * 4/44 = 0.167676767676... = 16.77% | |

Note that a in the above example is

**not** the same as hero's equity. a only denotes the cases where villain doesn't hit. Hero's equity is of course 100 - 16.77 = 83.23% so the difference should be obvious, namely that we still need to add c and d (the scenarios where villain hits but still loses) to reach hero's equity.

Hopefully that clears things up a bit