$90 would be my bet, but it can be improved
Slim, you arrived at my likely bet at the table, using much of the same thinking...
For a moment, assume bets must be in increments of $5, which is typical. I expect that Slim assumed the same.
Player A can get to $450 with a double down, so I need to get to $455. I'll bet $90. If I figured the fact that it locks out a blackjack by Player X, all the better. While that would probably cross my mind, I wouldn't waste any effort calculating it, because I know I've bet the least I can to cover A's double. If that doesn't lock out X's blackjack, oh well, I can't afford to.
Well, I managed to make a mistake in this example and as a result I still haven't illustrated the subtlety that Joe intended when he posted.
I intended $95 to be the best bet, but I changed Player X's bankroll at the last minute and mangled that, because $95 doesn't lock out the Player X blackjack.
All is not lost though...
At the Frontier, you can bet in increments of 50c, using the $1 and $2.50 chips. While I didn't intend to require that in the answer, I'll use it now to fix my mess.
You can actually bet as much as $94.50 and still lock out a Player X blackjack. Betting a little over $90 is better than exactly $90 for the following reason:
If Player A gets all his money working (split and double for less), and Player B gets a blackjack, Player B has it covered without doubling. With a $90 blackjack, he just ties A's all-in win. So the best bet is $90.50 to $94.50.
No way am I coming up with that bet at the table! Kudos to 'YMe' for coming up with that answer in an identical scenario posed during a chat at Global between rounds on Sunday.
Joe, sorry about hijacking your thread. I intended to just respond to rookie's post, and then I got carried away. Then, when I mangled my own example, I felt it necessary to clean it up.