+QA-Allan wants to know more about odds.
Dear Annie:
I’ve always been curious about this. Lets say I flop a flush draw. I of course have 9 outs to catch it. The advice from your brother was to multiply 9 by 4 to get a pct. of roughly 36 to get it. But is that assuming that all 9 cards that you need are still in the deck after say, its heads up between you and an opponent in a 10 player game? There are 19 cards(16 hole cards of opponents who folded and 3 burn cards). Isn’t reasonable to assume that maybe 3 or 4 cards that you need or in those 19 cards and you would only have maybe 5 or 6 outs? The pct. would go down then. Or am I mistaken and that is calculated in the 36 pct? I would really appreciate your answer as I really respect you as a player.
Thank you.
Alan
Hi Alan
I understand your confusion but in calculating odds the other cards don’t factor in. Let me explain:
The 2 and 4 rule are just shortcuts for estimating the odds. The long way around figuring out odds has to do with a few factors: The number of cards you know about, the number you haven’t seen, the number that help you and the number of cards yet to come.
So let’s take the flush draw example. You have J9h and the board is AK2 with two hearts. You know you need to hit a heart to win and there are 9 hearts left in the deck. What I mean by that is you have actually seen 4 hearts and you have not seen 9.
The fact that other hands that folded might have a heart in them is irrelevant because the fact you haven’t seen them means they might be live in the deck. You are just calculating on the cards that are still out there, that you haven’t seen.
Ok, so there are 9 cards that are good for you. You know exactly what 5 of the 52 cards in the deck are…those are the cards you have seen in your hand and on the flop. That leaves 47 cards that you haven’t seen, for 47 unknown cards. Of the 47 unknown cards you know that 9 of them help you and 38 of them don’t, right? So there are 38 bad cards left compared to 9 good cards left. If we reduce the fraction it is about 4.2 to 1 if you only get to see one more card, or right around 18% (notice that is 2 X 9). If we get to see two cards we can basically divide in half for 2.1 to 1 or right around 34%.
The fact is that of the unknown cards, the ones that help you and the ones that hurt you, they are likely to have been in the hands that for thrown away or the ones your opponents still have in equal ratios. There will be 4 good cards to every 1 bad card in all the unknown cards, the ones in the hands, the ones in the muck and the ones in the deck. We are concerned about the ratio when calculating odds and that is the same throughout all the unknown cards.
I hope that explains it
Xo
Annie