Are The Odds Identical Here?

[Nalapoint1]

If you hold AK or 72 are the odds of a 7 or 2 by the river the same as an A or K by the river?

[KJL]

Yes.

[LesWormMurphy]

You could say your just as likely to catch a 7 and 2 as you are to catch an A or K, but when the community does not hit, which it often won't-- AK will win, not to mention AK is more likely to make a straight.

So no, you don't want to play a hand like 72.

[Nalapoint1]

If I look at 100,000 hands will a 7 hit the board by the river about the same amount of times as an A?

[KJL]

Yes, if you have 72 a seven will hit about as many times as an ace will hit if you have AK. But that does not mean you will win just as much. Because there is a very good chance that an overcard will hit when you pair your sevens, and that is clearly not the case with an ace.

[Cerril]

That's a complicated question. If you were to deal out 100000 hands at random you'll see as many 7s as As on the board, but if you were to look at a 100k sample of actual hands you'll probably see fractionally more aces for the sheer fact that people chase aces more and play hands with aces harder on average, so more hands that are played to showdown will involve a paired ace. It's not going to be a huge disparity, but I bet it'd be there.

That said, about 35% of the time you'll see an ace by the river in boards with totally random hands, 35% of the time you'll see a seven, and about ten percent (plus or minus)you'll see both an ace and a seven. (so figure it's split -very- roughly along a 25/25/10/40 line for A, 7, A+7, neither).

Or in a more telling way to look at it, a reasonable amount of the time someone pairs up their 7, someone else pairs up their ace.

[TomCollins]

I would say its the other way around. Suppose you "know" an ace is coming on the river. That means that there are only 3 aces left for someone's hand. So the chances of someone still being in by the river is less, as they would have folded preflop. This means an ace is less likely to hit than a 7. It has to be very marginally different.

[Nalapoint1]

Thanks for the resonse guys. I thought that it was basically even but what prompted the question is my observation while playing party for the last 12 months. It seems that an A or 7 will be on the board by the river more often than any other cards.

I cant tell you how many times I have won with 72 or 75 and 7x from the BB when I can play the flop for free.I get berated and called all kinds of names but for some reason these people dont understand that if they raise I fold those hands everytime.

[KenProspero]

A different way of putting it is

Given 5 consecutive cards on the board, the odds are exactly equal. However, with at least 1 player holding 72 (and the rest of the cards being random) there is a greater chance that you won't ever see the river card than with at least 1 player holding AK

[ QUOTE ]
Thanks for the resonse guys. I thought that it was basically even but what prompted the question is my observation while playing party for the last 12 months. It seems that an A or 7 will be on the board by the river more often than any other cards.

I cant tell you how many times I have won with 72 or 75 and 7x from the BB when I can play the flop for free.I get berated and called all kinds of names but for some reason these people dont understand that if they raise I fold those hands everytime.

[/ QUOTE ]

Whoa whoa, all 13 card values have an equal chance of being on the board.