Opponent’s options: ROISTER/RIOTERS/ROYSTER/STROYER 3f, ROYSTER/ROISTER/STROYER c1, ROSY 11h, (R)OILY 2f
Candidate plays: TAX i5 (10), GANE 3l (25), AGA 3k (21), SAIGA 3i (27), AI 13f (7)
Potential plays on next turn: EASY 11h, bingos that play in two spots (AGONIES, REGINAS, INGATES, etc.), potential out plays
Subgoal: Make the play that wins the most game by assuming a random two tile draw.
Resolution: It’s worth immediately noting that blocking bingos is pointless, as there are only a few bingos in this pool and all of them bingo in two spots. If II or IY is in the bag, you’re not going to win. Because of this, we can just disregard the bingo as a possibility with all plays except TAX.
The best way to go through these choices is the process of elimination. AGA and GANE because it neither bingos nor provides outplay potential: AIS doesn’t go out very often with this pool (compared to EN). With draws like IR, SAIGA is the only play that will win by going out next turn.
Comparing AI and TAX is a little bit harder. TAX will result in a bingo only 4/9 of the time, but will also win a fair amount of the time when it does not bingo. However, leaving one in the bag is also a curse, against a good opponent: it gives them an opportunity to fish, so if you miss your bingo you usually won’t win. For instance, if you draw the Y, and your opponent has EIIRRST, they will fish off the I and win when they draw the O. This kind of game would be won after AI. Because of this factor, AI is a better play: you will lose a lot of endgames after TAX where you miss and they hit. Also, the letters that you need to bingo (RRTO) are letters already in their bingos, thus, when they bingo you will always miss. For these reasons, AI is superior.
Comparing AI and SAIGA requires permuting through sample draws and looking for draws that win under one scenario but lose under the other. For example, an IO draw loses to SAIGA (TRIER), while an IS draw will lose to AI (YORE) or OT (IRIS). If you go through all the possible draws, you’ll see that SAIGA is a slightly better play, though AI is also strong.