In his stream of a lesson to Jerni at 38:45 while playing a mass WW and Grand Market deck SCSN says that you should always play wishing well first because then if you wish wrong you can pick up the missed card with the GM. I had thought quite the opposite and was wondering the whole time why he kept playing WW instead of GM first. My thinking is that the more other draw cards you play first, the more information you have about the rest of your deck, and therefore the more accurate your wish. So say that you have a deck full of WW, silvers, and GM. Your hand has 1 GM and 1 WW. Which do you play first?
My thought is play GM first because then when you play WW you will have more information about your remaining deck composition. By this method you draw 1 from GM, 1 from WW, and 1*P(guess right) from WW. SCSN says to play WW first because then if you're wrong you can draw the remaining card with GM. By this method you draw 1 from WW, 1*P(guess right), and 1 from GM. So I don't see how playing WW first is the better move. As far as I can tell you are more likely to guess right and draw more cards by playing GM first.
So what are your thoughts on this? I'm especially interested to hear from SCSN, since he was the one who made the original claim with which I disagree. Am I missing something?
It depends on what you need. Playing GM first maximizes the odds of a correct guess, and thus the number of cards you will draw on average. However, that's not always what you need: playing WW first allows you to "buy insurance", reducing your best case in exchange for improving the worst case.
Suppose you have remaining in your deck two Coppers, a Market, and a Province; in hand are a Market and a Wishing Well.
If you need to draw all three money cards to win the game, you play the Market first, then play Wishing Well, and wish for whatever money card you haven't yet drawn (succeeding if the Province is the bottom card of your deck, or if you drew the Market soon enough to draw all four cards). This is clearly superior to playing Wishing Well first, because you would have to guess among three cards instead of two.
However, what if you only need two money cards? Then playing the Market first leaves you in danger: you might draw a Copper with your Market, then draw Province with Wishing Well, and be stuck on a 50/50 guess for the last card. Instead, play Wishing Well first.
- If you draw the Market, then anything works: you are guaranteed the $2 you needed to draw, and you can choose to wish however you like.
- If you draw Province, you should wish for Copper: either you are successful and get a Copper plus another guaranteed money-card draw from your Market; or you miss, but your Market draws the Market which is on top of your deck, and then you get another Copper.
- If you draw a Copper, then wish for Province. If you hit it, your Market draws you another money card (and maybe two); if you miss, then your Market draws whatever money card was on top of your deck instead of Province.
Cases (2) and (3) above are conceptually the same, and don't really need to be argued separately, but are enumerated for completeness.
Edit: The same sort of argument can apply to a larger deck, eg if your "maximum" draw is overdrawing your deck, you can sacrifice some of the wasted extra draw in order to be more certain of drawing your entire deck.
Further Edit: So the rule of thumb I use is: if I need great draws, then I'll play the non-wishing cantrip first (here, GM), and then use the wishing card to pick up whatever it is I still need. If mediocre draws will suffice, and I want to ensure against really terrible draws, then I wish first, and aim for bad cards. If I successfully hit them, then I've avoided the bad turn I was going to have; if I miss, I get a decent turn anyway because I didn't have junk on top of my deck.
Maybe SCSN plays so well that mediocre draws will always suffice to win the game: that would explain why his rule of thumb is "WW first always"!