Odds question

corblimey

Can somebody who's better at maths than me (ie everybody) work this out.

I've got A9o on a board of A74. I'm against 1 opp. What are the odds that

a) he's got an ace
b) he's got a better ace (ie, A4, A7, AT-AA)

If another ace comes on the turn, how do those odds change?

ronanp

Do you mean the odds of him having been dealt an ace, or the odds of him holding one now? They're different questions! Assuming its the former, how many people are at the table?

corblimey

ronanp wrote:

Do you mean the odds of him having been dealt an ace, or the odds of him holding one now? They're different questions! Assuming its the former, how many people are at the table?

The odds of him getting a ace are different to the odds of him having an ace??? Wow, that's odd (pardon the pun). I'm not sure which I want now.

It's a full ring table, 9 players

mewso

I always get these wrong but here goes:-

8% chance he has one of the 2 remaining Aces.
If he has one of them then it's 48% that he has you beat.
If an Ace comes on the turn then it's about 4% he has the last one. If he does have the last one hes about 48% again to have you beat but 50% if the turn didn't remove one of his outs. O.k. time for the experts to step in and correct me.

Mellor

corblimey wrote:

The odds of him getting a ace are different to the odds of him having an ace??? Wow, that's odd (pardon the pun). I'm not sure which I want now.

It's a full ring table, 9 players

The odds of him getting dealt an ace are based on pure maths. The number of aces lft in the deck, and the number of people affect the odds.

The odds of him holding an ace in this situaton are different though, as he is more likely to play an ace hand, than say 3,6.

so 47 cards, 2 aces, 16 cards being dealt.
there are 47[c]16 ways to deal the cards
and 45[c]16 ways for no aces to be dealt. this is about 43% of the time.
So somebody can be dealt an ace 57% of the time. (this includeds the time where more than one peson is dealt an ace)


and if he holds an ace. there are 46 other cards he could hold. 20 are worse aces, 23 are better and 3 are equal.
Worse Ace {20/46} 43.5%
Equal Ace {3/46} 6.5%
Better ace {23/46} 50%

So assuming that someone was dealt an ace 57% of the time, these %s become
Worse Ace {43.5%} 24.8%
Equal Ace {6.5%} 3.7%
Better ace {50%} 28.5%


But this assumes that players will play any ace from any position. In practice, when you will see aces at the higher end of the scale more often than the odds suggests, this is probably outweighted by the fact that two betters aces a4 & A7 are low and not always being played. And if he chooses to play on it also increases his chances of having an ace.

Mellor

sorry, forgot the next bit, if an ace come on the turn it changes alot
46 cards, 1 aces, 16 cards being dealt.
there are 46[c]16 ways to deal the cards
and 45[c]16 ways for no aces to be dealt. this is about 65% of the time.
So the last ace only gets dealt out 35% of the time preflop. and he has you beat about 17% of the time.


musician's odds are based on if the lone villian has an ace. my way works of based on weither anyplayer was dealt an ace preflop, assumes that the ace was played. Thats why its important to know how many players are playing, as heads-up versus full table makes a hugh difference.

corblimey

Thanks Mellor, v.detailed.

mewso

Mellor wrote:

so 47 cards, 2 aces, 16 cards being dealt.
there are 47[c]16 ways to deal the cards
and 45[c]16 ways for no aces to be dealt. this is about 43% of the time.
So somebody can be dealt an ace 57% of the time. (this includeds the time where more than one peson is dealt an ace)

Makes sense but I thought the question was about 1 player in particular having an Ace not the chance of 1 of the other 8 having one so surely you need to divide this number by 8?

mewso

Mellor wrote:

musician's odds are based on if the lone villian has an ace. my way works of based on weither anyplayer was dealt an ace preflop, assumes that the ace was played. Thats why its important to know how many players are playing, as heads-up versus full table makes a hugh difference.

sorry just spotted that. My calculations were slightly out on the strength of the ace as I forgot to subtract the opponents other card so I was doing 23/47 insead of 23/46.

Hectorjelly

this is a totally useless question, unless the guy isnt looking at his cards he has made a decision preflop which is going to heavily weigh the odds towards his having an ace. Similarly, if a guy calls a raise preflop, and then a bet on an ace high flop and theres an ace on the turn, the chances of him having an ace if his hand is random is very small, but because we have other information, ie his calls, the chance is actually quite high.

Mellor

Hectorjelly wrote:

this is a totally useless question, unless the guy isnt looking at his cards he has made a decision preflop which is going to heavily weigh the odds towards his having an ace. Similarly, if a guy calls a raise preflop, and then a bet on an ace high flop and theres an ace on the turn, the chances of him having an ace if his hand is random is very small, but because we have other information, ie his calls, the chance is actually quite high.

I'd agree, I tried to point that out to the OP. The difference between being dealt an ace, and the villian having one in a given situation is huge.

Calculating odds in poker shouldn't be done this way.
But new (and bad) players tend to overvalue Ax hands. Above posts should show them that at a full table, when you are dealt an ace, more often than not somebody else has been dealt one. So rethink the strength of medium aces.

corblimey

My question was based on a real life issue. I was in the BB and the villian had raised to 3BBs from EP. Due to other information and previous betting patterns, I put him on an ace, but he had played with any ace in this position in previous hands, so after he pushed on the turn and I called (for about half my stack), I was berated by the table. I felt like his push was proof that he hadn't a house so my set was beating him about half the time and it was a correct call in that situation.

As it was, he had AJ and niether of us improved.