AA v. str8/flush draw

[remi983 0]

Hey guys, I really am having trouble grasping this concept and I need some help. How come a come hand with 15 outs is a favorite over a made hand that can't improve? For example: AsAd v. 5c6c with a flop of 7c8c2h - the connectors are a favorite to win, why? There are 45 cards left in the deck, 15 will help the aces (2 chances to catch 15 cards) and the other 30 remaing cards will leave the aces ahead (really 30 after the flop and 29 after 4th street).Every book I have read tells me that the st8/flush draw is the favorite, and I play like they are - but I really dont get it; can someone please explain the math to me?

[Smasharoo 0]

Sure, two shots at 15 outs in a deck of 47, then if you miss, 46 cards.So...47/15 + 46/15 gives you the chances you'll draw out by the river.If you miss on the turn, AA is again a large favorite.I know it's counterintuative, bcause AA has more cards in the deck that keep it the best hand, but it's important to understand.If you had a two outer to the mortal nuts and they dealt out 40 river cards, you could see how you'd be a favorite there with the drawig hand, no?

[mgross 0]

Sorry, but I do not think those odds are exactly correct because it double counts "if you hit on the turn." So the odds of that addition will be slightly higher than the real odds. I think the real odds are 1 - (the odds of not hitting on the turn or river).So, if you have 15 outs,1 - ((32/47)*(31/46)) <--- I think that would be the correct odds of hitting one of the 15 outs on the turn or river. = 1 - 0.4588 = 0.5412Whereas the previous post's odds say it is:= 15/47 + 15/46 = 0.6452But, even if you hit on that 0.5412 chance of getting a flush or a straight, those are still not the correct odds of winning. This is because you can still lose to a full-house or 4 aces, even if you hit your straight or flush. I am not going to calculate those odds, but I imagine that they are quite small, and it depends if you hold an ace or not or if he holds an ace of the suit you need for your flush, etc... So, this brings the probability of you "winning" the hand even closer to fifty percent. So, really, in my mind, this is a toss-up even though if you play a million of these hands and call "all-in" every time, you will be ahead. Please let me know if my math is off. I would greatly appreciate it.

[Smasharoo 0]

But, even if you hit on that 0.5412 chance of getting a flush or a straight, those are still not the correct odds of winning. This is because you can still lose to a full-house or 4 aces, even if you hit your straight or flushUnless you deal an extra card it's going to be kind of tough to hit the straight and loose to a FH.Your math is right and mine is wrong, though.

[remi983 0]

Thanks guys, i think the odds for the str8 or flush are higher, though:52 cards minus 4 cards(2aces and 5c6c)minus 3 cards (the flop) = 45so, the total remaining cards are 45 and 44, not 47 and 46Still, is it profitable in the long run to continue with the draw if I dont pick it up until the turn?

[Smasharoo 0]

Still, is it profitable in the long run to continue with the draw if I dont pick it up until the turn?Depends on how much is in the pot, if you are playing limit or NL, if people will call bets when you hit and about 90,000 other things.Ussually yes, though.

[wookie 0]

Thanks guys, i think the odds for the str8 or flush are higher, though:52 cards minus 4 cards(2aces and 5c6c)minus 3 cards (the flop) = 45so, the total remaining cards are 45 and 44, not 47 and 46Still, is it profitable in the long run to continue with the draw if I dont pick it up until the turn?

not true - since you are not aware of the contents of your opponents cardsin the moment, you have to use the larger denominators.the good news is that these odds apply to a lot of 'made' hands, but notknowing your opponents hand also means that a paired board shouldcause concern. that said, having a draw to both a straight and aflush on the flop is about as good as it gets...- w

[Shaffer 0]

The math described by mgross is correct ... your odds with 15 outs and 2 cards remaining, against a hand that cannot improve (or has an extremely minimal chance of improving, such as hitting your flush with runner-runner aces) are roughly 0.8 to 1 in favor, or roughly 56%. IMO this is an automatic call even for all-in unless you are a very substantially better player than your table. At my home game, I will occasionally shy away from calling all-ins with powerful drawing hands, particularly if I'm up against a weaker player where I won't have a problem taking their money when I've got a made hand. In limit poker this should obviously always be an automatic call, and often a raise.The way to look at this without getting deep into the math of it is this, I think: look at it from the perspective that for you to miss, BOTH remaining cards have to miss. The odds of either of the two cards hitting individually are relatively small, but the odds of both of them missing are not great either.

[Fira 0]

Since you have trips, you're not that much of an underdog... about 40-60, since you can make a full house or maybe quads on turn and river if they make their flush or straight.