[Help me!] Odds and Outs

[PSMatt]

hey,
this is a noob question but im trying to figure out how to get odds against 1 (?:1) from the number of outs you have and what the calculation is to get this.

I know 5 outs is ~4:1 odds but how do you get to this, do you have to work out the % then work back to the odds ratio?

[MadMojoMonkey]

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.

[PSMatt]

ok i think i got it could you do another example for 9 outs after the flop.

[PSMatt]

actually the more i think about the more confused i get is 9 outs is 36% how do i make that a ratio i have no idea lol.

[MadMojoMonkey]

9 outs * 2% is 18% to catch on the turn. 18% for Hero leaves 82% for Villain.
82/18 ~= 4.5:1 against

Same calculation for the river.

If Villain has pushed all-in on the flop
9 outs * 2% * 2 cards = 36%. Hero has 36% so Villain has 64%.
64/36 ~= 1.8:1 against

EDIT: If Villain is not putting you all-in on the flop, the 36% is completely useless. DO NOT bet or call for the odds on 2 draws when you have to face another bet after the first draw. If you're shoving the flop with a FD, then you KNOW you're behind and you're counting on fold equity to make your move +EV.

[d0zer]

Odds are usually specified as "odds against winning", and it's a ratio of loseOutcomes : winOutcomes.

So for 36%, you have 64 outcomes losing and the other 36 winning (from 100 cuz percent).

64 : 36 or 1.78~ : 1 reduced.

[PSMatt]

ok awesome thanks for the help!