[CORed]

[ QUOTE ]
The HA of the pass-line bet does not change, of course. The HA of the game as a whole (played optimally) does change- which is what I was talking about. If he said the HA of the pass-line bet does not change, you would be correct. However, he said the HA of craps does not change, which is incorrect.

[/ QUOTE ]

The odds bet in craps is a 0 EV bet (assuming fair random dice and no ability of the shooter to affect the odds through skilled shooting, of course). Therefore, placing an odds bet does not change the HA in dollars. It does, however, reduce the HA in terms of the percentage of your total wager. In the long term, it increases your variance without changing your EV. Making a $5 pass line bet with $10 odds is better than putting $15 on the pass line, but the same, in terms of EV as making the $5 pass line bet without the odds bet.