A question of probability

Here's one that I read about elsewhere on the web.

I apologize for the notation I am using but it is simple enough.
Here are the two relevant hands:

Hero: Q-Q
Villain A-Q

Flop: 5-6-Q

The question is what are the odds on the next two cards being the aces that Villain needs to win?

The estimates I have seen range from 22-1 to 400-1, and another estimate from an odds tool that suggested Villain has a 0.95% chance to win. (The point being that he did draw the cards he needed.)
So what are the odds? Your thoughts please.

Well, there are 52 cards in a deck, and you know 7 of them. So now there are 45 unknown cards containing the two aces opponent needs to win.

The probability of hitting an Ace on the turn AND river is a multiplication problem. So, 2/45 (2 aces in the deck of 45) X 1/44 (the one ace would then be known and now there are 44 cards) x 100 = .101%

In ratio notation its like 989:1

This is of course ignoring whether or not villain can hit a flush since no suits were listed in your example.








[I think]

Fatguy - we know of only one Ace, which means we have three aces we can bink on the first draw, and two o nthe second.

3 aces out of 45 unknown cards: 3/45 on first draw
2 further aces out of 44 unknown: 2/44 on second draw

(3/45)*(2/44) = 0.3030% or about 330 to 1.

Course I rarely use anything but pokerstove to calculate shit like this anymore and maybe I've just gone full retard on how these calculations work. LOL.

FWIW whoever this happened to should quit their bitching, trying to figure out how unlikely it was they would be beat. Time better spent elsewhere.

That's one hell of a bad beat. The good thing is you win this the other 329 times so when it happens, just be happy you got it out of the way.

Yeah, so I just got home and ran this situation on poker stove - the odds I listed above are correct - about 330 to 1 (0.3030%)

The worst beat possible in holdem is when Villain has 2 outs to hit and must hit both of them, ie AA v QQ on A64.

I very clearly remember the first time this happened to me.

Originally Posted by Penneywize

Fatguy - we know of only one Ace, which means we have three aces we can bink on the first draw, and two o nthe second.

3 aces out of 45 unknown cards: 3/45 on first draw
2 further aces out of 44 unknown: 2/44 on second draw

(3/45)*(2/44) = 0.3030% or about 330 to 1.

Course I rarely use anything but pokerstove to calculate shit like this anymore and maybe I've just gone full retard on how these calculations work. LOL.

FWIW whoever this happened to should quit their bitching, trying to figure out how unlikely it was they would be beat. Time better spent elsewhere.

^this

Text results appended to pokerstove.txt

8,910 games 0.005 secs 1,782,000 games/sec

Board: Qd 6h 5c
Dead:

equity win tie pots won pots tied
Hand 0: 00.303% 00.30% 00.00% 27 0.00 { AQo }
Hand 1: 99.697% 99.70% 00.00% 8883 0.00 { QQ }

I knew something was off cause of the stove results, I guess I forgot there are 4 aces in a deck , thanks penney.

Originally Posted by fatguy'06

I knew something was off cause of the stove results, I guess I forgot there are 4 aces in a deck , thanks penney.

LOL np, happens to the best of us.

..

Originally Posted by daven

um, wtf at everyone in this thread. If turn = ace and river = ace then villain has trips, and hero has the nut full house.
the only (as per stove) chance of villain winning is some flush thing happening.

QQ on xxQAA is QQQAA, AQ on xxxQAA is AAAQQ

Haha got you before the edit

Originally Posted by spoonitnow

QQ on xxQAA is QQQAA, AQ on xxxQAA is AAAQQ

damn you're fast
i mis-read and had already deleted

Originally Posted by spoonitnow

The worst beat possible in holdem is when Villain has 2 outs to hit and must hit both of them, ie AA v QQ on A64.

I very clearly remember the first time this happened to me.

i've actually been runner runnered twice in a row before. One time i had a set and the other dude just had a pocket pair but he made quads by the river. Then on the next hand against the exact same guy he hit a back door flush on me. Both times i got him all in on the flop as a huge dog and both times he sucked out. Happened at titan before the uigea.

sejkbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgzdfmbfd

Originally Posted by kiwiMark

sejkbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgzdfmbfd

pretty sure this is kiwi-speak for "I approve of this thread"

penney did you get your name from the stephen king novel. I think it was called the it

Thanks a lot guys for the input. I realize the question that I asked could be understood in different ways. I was actually asking what were the odds of the event happening and not just the odds as seen by the players.
For those that were wondering there was no option for a flush.

Thanks a lot guys for the input. I realize the question that I asked could be understood in different ways. I was actually asking what were the odds of the event happening and not just the odds as seen by the players.
For those that were wondering there was no option for a flush.

What's the difference between the event odds and the odds as seen by the players?

By event odds I meant 'what were the chances of the next two cards being aces after the flop?' However, that takes into consideration the fact that we know two of the aces are already out there. (A very non-poker way of looking at things.)
The odds as seen from the players point of view the players, and in particular the villain who can only see the one ace in front of him.

I have no idea what you just said.

If it's any consolation, I doubt getting the answer to your question is gonna help you out at all.

Originally Posted by Tasha

By event odds I meant 'what were the chances of the next two cards being aces after the flop?' However, that takes into consideration the fact that we know two of the aces are already out there.

I'm not sure how this is any different from what was already explained. We provided the odds of: knowing that one ace was already 'out', and that there were 45 unknown cards on the flop (two in hero's hand, two in villain's, and three on the board after the flop, out of a deck of 52), how often will both the turn and the river come an ace. In this case, the odds are as stated above, 0.3030 or ~330 to 1.

Originally Posted by Tasha

The odds as seen from the players point of view the players, and in particular the villain who can only see the one ace in front of him.

The odds of winning against QQ as seen from the player holding AQ on a board of x-x-Q are as detailed above.

As for the player holding QQ on such a board, if they are really concerned about the turn and river coming aces, they would also have to include an Ace in villain's hand; as such the calculations are pretty much the same -- depending on whether we treat the villain's second hole card as unknown or not.

If, for whatever reason, the player holding QQ would like to arbitrarily calculate the probability of the turn and river coming aces when he or she has no information on villain's hole cards, the odds are (4/47) * (4/46).

If you want to know the simple probability of a turn and river both coming aces, when we have no information on anyone's hole cards, the odds are (4/49) * (3/48).