flop odds

here's the general idea of the situation: i have JJ and opponent has AQo. i raised, opponent reraises, and i'm trying to decide whether to go all-in preflop or try a stop and go play.

i'm trying to figure out some mathematics, specifically the probability of an A or Q falling on the flop. i did:

6/48+6/47+6/46

is this correct?

Not quite, no. Because you're worried here about any one of two different cards falling on flop, you don't simply calculate it by each card as shown. Instead you calculate it as the chance none of them will happen then subtract that from 1 to get the chance the situation will happen.

Now your question is only specific to flopping an A or Q, nothing else. There are six cards in your specific question, three aces and three queens. Three is also one other thing we have to factor in and that is that you actually know your opponent has AQ.

So this then becomes:
1 - (42/48*41/47*40/46) = 1 - .6637 = .3363 = 33.63% that an A or Q will fall on the flop.

33% it's ok but you're not considering all the posible situations, like for example a J coming on the flop turn or river that could give you trips, or some other series of running cards like: A9T 8 7 etc.

For all the situations you're chances of winning the hand if you go all-in preflop are 57%, against 42% of you're opponent.

1,712,304 evaluations, 1 hole card combos
Pre-flop
Wins Ties Equity
42.87% 0.20% 43.08% ( AsQh )
56.72% 0.20% 56.92% ( JcJs )

it's a stop and go play so i'm not worried about preflop odds..

Jack is right. do that. or, JJ is probably good PF, so get it in. All of it. If he calls, he has made a mistake, and you win, even if you lose.

wow, very well said on the second post. good anser to his question, easily figured out. Thanks

so if you have 57% chances of winning preflop and there's only 33% chances for an ace or a queen to flop, you can say that the stop and go is the more profitable move right?

yeah I can follow ando's logic. but that's if you know your oponent's hole cards. an Ace, Queen, or King is the same thing-and over card that you must respect. so that makes it 10 cards left in the deck you don't like if they flop. 6 from AQ, AK, hands and then the other 4 Kings or Queens or whatever he is not playing. so 1-[(40/50) (39/49) (38/48)]=0.499 approximately. the good old fashiond coin flip. i like shoving pf. further more he might not put the rest in post flop unless he hits. even further more, depending on the stack sizes, you might only able to price him in with a flop bet if an A, K, or Q does not flop. He needs like 3.33-1 to call and hit by the river. something more to think about. peace

in a cash game, yes, but in a tournament that's not always the case

When is it not always the case? And Why? I'll tell you: around the bubble and at the final table when you want to avoid colliding with another big stack ending yourself up in a coinflip situation when the next rank up pays a whole lot more than what you will get if you bust right now. I understand what your saying. You want to play in a way that reduces your variance as much as possible, but your still playing poker. Which is gambling. A poker tournament can be seen as finding out who is the best gambler when gambling in the form of poker times who gets the most lucky. fight that urge to be totally sure you are ahead in the hand like if your studying for a chemistry test or something. you will almost never be 100% in poker. so look at the math and just get it when its probably good.

What you also must consider is the table image of the guy that's re-raising you! There are one or two players I know that are so tight that I would fold jacks in a heartbeat if they re-raised me heavy enough, and others that 90% of the time will re-raise a button steal out of habit with total junk, or at best a raggety ace. Jacks are always hard to fold pre-flop, but to a solid player they are at best in a race situation and a marginal favourite, but can of course be outgunned by queens or better. Your odds on pushing are therefore between 20% and 55% if they have a valid re-raising hand. There are also the people that think nothing of re-raising all-in with a small or middle pair, so you just have to make your choice based on your observations on their play.