Quote Originally Posted by krimson
It seems that many of you think that the differences between 65s/76s/87s against AA in some way related to them blocking or dominating the possibilities for AA to make the wheel (or straight-flush versions thereof). This is actually completely wrong.
Story time: A few months back I decided to write my own poker number-crunching programs. I used AA vs 76s as a test case while debugging. In my first drafts I didn't bother including the extra lines of code necessary to allow A to play low in a straight. When I did add the code I at first thought I had got it wrong: the output for AA vs 76s did not change at all!
But when you think about it it makes perfect sense: there really is no way that AA will beat 76s with a straight (or straight flush) it it could not also beat it with a pair of aces (or a flush). If we changed the rules so that you cannot play an A at the low end of a straight the win/tie/lose probabilities for AA vs 76s would stay exactly the same. So the wheel really is not the issue here.
What's actually behind the differences in win/tie/lose probabilities between 65s/76s/87s against AA is that the lower ones are more likely to have their straights counter-feited by board straights, so they are slightly less likely to win. On the other hand it is more likely that there will be some board straight, so they are more likely to tie.

Quote Originally Posted by Bailey
which is why TJs would win a few more times against 22 then 9Ts would
There's also good ol' high card power. JTs is more likely to play its kicker on a two pair or quad board, less likely to have boats counter-feited etc.
Great post. I didn't think of this myself. I think I've finally cracked this puzzle.

1. 56s is more likely to tie than 67s than 78s. This is because more central cards (7s and 8s) remain in the deck and therefore more board straights available. 67s is the second most likely to tie, and 78s the least likely out of all three.

2. 87s is more likely to win than 67s than 56s. This is not because of straights being counterfeited (that makes no sense). The reason is because of *flushes* being counterfeited. If you hold 87s, then the only board flush and tie by coming AKQJ10, AKQJ9, and AKQ109 (all in the suit of the connector). Any other possibility gives the 78s a straight flush. But as you go down to 76s and 65s, there are a lot more ways (like AQ1097 spades coming down then you hold 65s is a tie, not a win for 65s.

3. 87s is more likely to lose than 67s or 56s. This is because one of the straight boards made by 87s is actually a loss (9 10 J Q K).

So there you go. Mystery solved.

Also, can someone verify that the lowest pre flop hand that can be the stone cold nuts on the flop is indeed 26s and not any of the other answers given?