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Yes, you find the %-age, then translate that into odds.
On the flop, you can see 5 cards from the 52 card deck, so there are 47 possible turn cards, and then 46 possible river cards. You take your number of outs and divide by 47 to catch on the turn, and similar with 46 for a river draw.
So 5 outs on the flop is 5/47 is 10.6% to catch on the turn. If you miss the turn and your hand is not otherwise improved, you will have 5/46 is 10.8% to catch your card. 10% for Hero leaves 90% for Villain, which makes Hero a 9:1 dog.
Notice that 5 outs is ~10% whether you're drawing to the turn or the river. This is because dividing by 46 or 47 is not too different than dividing by 50, and 1/50 is 2%. So a quick estimate of your % chance to catch is simply #outs * 2%. This is an under-estimate, but the error is slight.
You cited the odds with 5 outs as 4:1, which is assuming you get 2 draws to catch your 5 outs. 5 * 2% * 2 (draws) = 20%. And that leaves 80% for Villain, which makes Hero a 4:1 dog.
Also notice that it doesn't serve you any purpose to know the odds of catching your cards in 2 draws, unless you're calling an all-in bet on the flop. Otherwise, you need to think of it as 2 separate situations, one on the turn and one on the river.
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