Nearly Everyone I Know Who Plays Scrabble

...is the type to play STRAIN when his rack is SETRAIN. So I don't know who to turn to with this "problem" I encountered yesterday.

My opening rack was ZONORS?. I went first. I haven't checked Quackle or similar but I'd hazard that SNOOZER is the only bingo here. So the only choice is whether to play the Z on the DLS (and thereby open myself up to a SNOOZERS/something two-way TWS, which kinda sucks enormous dick), or play it in some other fashion. The former is worth 100 points, the latter is worth 82.

Of course, it's not like my opponent is a lock to have an S or a blank, especially since I am using two of them in my bingo. So there's a (4/93)*(7) chance that he draws an S/blank, which is ~=.30. (This probability is the same for me, but he gets to "go first.") So 30% of the time he can play a word that will, on average, be worth 16 (value of SNOOZER(S)) + 9 (seems like a decent estimate of the EV of the word he can play vertically, factoring in the times he can only play TUNES with the times he gets to play JILTS or something similarly massive), all times 3 since it's all on a TWS. So 75 points, 30% of the time = EV of 22.5 points. This cannot be that far away from his "normal" EV, if I just play SNOOZER with the S on the DLS.

It seems like it would have been worth it to play the Z on the DLS, and go for the full 100 points. I do imagine that the correct play has a lot to do with the skill of the players involved -- both relative and absolute. Like, if I were playing someone that wasn't very good, I'd have to assume that starting out with 82 points would make me a virtual lock to win the game. So it would not make as much sense to go for 18 more points and give him a very good opening. Yet if the game featured two expert players, the thin edge becomes much more germane, and thus playing SNOOZER 8H has to be the correct move.