Originally Posted by Xmaster
55 and 66 have the same chance to make a straight...
If players were playing ATC, then maybe, but in reality, players are selective when choosing starting hands. I'll go over all my logic with you and you can point out which parts you disagree with:
I know that AA, 22 and KK are least likely to make straights, since there are only 2 combinations of straights involving them (22 has A2345 and 23456, KK has TJQKA and 9TJQK, AA has A2345 and TJQKA).
Then 33 and QQ have 3 combinations of straights (33 has A2345, 23456 and 34567, QQ has 89TJQ, 9TJQK and TJQKA).
Then 44 and JJ have 4 combinations of straights (44 has A2345, 23456, 34567 and 45678 and JJ has 789TJ, 89TJQ, 9TJQK and TJQKA).
Then 55, 66, 77, 88, 99 and TT have 5 combinations of straights each.
So it would appear as if 55 and 66 are equally likely to make straights... but you must now take blockers into account and the villain's likely range.
Which of these straights is the villain more likely to have? Is the villain more likely to have a "wheel" (A2345) or a 6789T straight? If you think that wheel straights are more common, then 55 acts as a more significant blocker than 66. And if it's a more significant blocker towards straights, doesn't that make it better in that aspect?
I'm talking about the probability of making straights and the probability of blocking straights, not just the former.