Quote Originally Posted by Thunder
My point being, with just 9 cards left (18%chance) and with $1282 in the pot, calling $282 to win $1564 is providing him with odds of 1 in 5.5 which is 4.5 to 1.
He's not winning $1,564. He's betting $282 to win $1,282. That's 4.5 (in the pot) to 1 (his bet). You're counting his wager in his winnings.

Again, his probability is 1 in 5.5, or 1/5.5. But his odds are 4.5 to 1.

Suppose there's $100 in the pot, villain bets the pot, and I have EXACTLY 1/3 chance of making the best hand with one card to come. Play it out three times.
1. I call $100, making the pot $300. Lose my $100 bet.
2. I call $100, making the pot $300. Lose my $100 bet.
3. I call $100, making the pot $300. Win $200 on my bet.

I've made a $100 bet three times, lost it twice, but won $200 once. Breakeven. This is 2 to 1 odds against me making my hand, since I win once and lose twice in every three rounds, on average.

Probability -- Odds against (of hitting my hand)
1/4 -- 3 to 1
1/5 -- 4 to 1
1/6 -- 5 to 1

And so on...