Last night on Jarvis Yu’s stream (check it out at twitch.tv/jarvisyu , it’s a good watch) a situation arose where he was priced into playing a blind Predict. He named a four-of without much thought as to which four-of to pick, and then some discussion ensued as to what the best play was.
TLDR: in a situation like that, where you're not likely to see a very large percentage of your deck by the time the game ends, the difference is really tiny. But let's look at some concrete maths, because I like this kind of little math puzzle.
First of all, let's simplify the situation to assume that there aren't particular graveyard effects (e.g. graveyard eldrazi shuffle triggers, flashback, etc.); let's also assume that we can narrow down the options to one card that's "good" and one that's "bad" (presumably the best and worst 4-ofs left in the deck). The first thing I want to do is show that, very concretely, there are some situations where naming the good card is optimal, and some situations where naming the bad card is optimal.
Scenario A: Your opponent is empty-handed. You've just untapped with a billion mana and only the predict in hand. A Sulfuric Vortex trigger just went on the stack which will kill you when it resolves. The only cards left in your deck are 2 Lightning Bolts and 2 Shocks. Your opponent is at 3 life.
If you name
Lightning bolt:
You have a 50% chance of guessing right, in which case you win on the spot (any 2 spells are lethal)
You have a 50% chance of guessing wrong. In this case a shock gets milled, and you draw 1 card out of a deck of Bolt/Bolt/Shock. This gives you a 2/3 chance of winning.
Overall, you win 5/6 of the time.
Shock:
You have a 50% chance of guessing right, in which case you win on the spot.
You have a 50% chance of guessing wrong, in which case you mill a Bolt, and draw 1 out of Bolt/Shock/Shock. This gives you a 1/3 chance of winning.
Overall you win 4/6=2/3 of the time.
So we can see in this scenario, it's better to name the better card (Lightning Bolt), which increases your win rate in this case by 1/6.
Scenario B: Exactly the same as Scenario A, except now your opponent is at 6 life instead of 3.
If you name
Lightning bolt:
You have a 50% chance of guessing right, in which case you draw 2 from shock/shock/bolt, which can't win. You lose.
You
have a 50% chance of guessing wrong, in which case you draw 1 card, can't burn them out, and lose for sure.
Overall, you win none of the time.
Shock:
You have a 50% chance of guessing right, in which case you draw 2 from Bolt/Bolt/Shock. You need the shock to be on bottom to win, which only happens 1/3 of the time, so you win 1/3 of these games.
You have a 50% chance of guessing wrong, in which case you draw 1 card, can't burn them out, and lose for sure.
Overall you win 1/6 of the time.
So in this version, it's better to name the worse card, which increases your win rate by... well the same 1/6 as it happens.
So we've established at least that scenarios can exist where it matters significantly, and that sometimes you want to name a better card, and sometimes you want to name a worse card. Let's quickly check a couple more cases similar to these; if instead the opponent had 4 life, you just need to draw 2 spells, any 2 spells, so it doesn't matter - you need to predict right to win, it's 50/50 either way. If they're on 5 life, you need to draw either bolt/bolt or bolt/shock; you want to name Shock here, which gives you a 50% chance to win (whereas naming Bolt would give you only a 1/3 chance).
But these scenarios are pretty artificial. What about other scenarios?
Scenario C: You're digging for one specific card which will win you the game, and you need to find it right now. Let's say you're down to 8 cards again, 4 Winners and 4 Losers.
If you name
Winner:
Guessing right gets you a 5/7 chance to win, and guessing wrong gets you a 4/7 chance to win, for an overall win rate of 9/14
Loser:
Guessing right gets you a 6/7 chance to win, and guessing wrong gets you a 3/7 chance to win, for an overall win rate of 9/14
So here it doesn't matter, which matches Jarvis's original intuition
Scenario D: Same as C, but we add 32 other 1-of blank pieces of cardboard to the deck. You still need to find one of the 4 copies of Winner to win the game. Now in this case, 32/40 of the time, a card besides one of your options is on top, and it didn't matter at all which of the two cards you named. So we only need to look at the 20% of the time where it actually matters.
If you name
Winner:
Guessing right gets you a 15.0% chance to win, and guessing wrong (with Loser on top) gets you a 10.3% chance to win, for a win rate of 12.6% in the 20% of cases it matters
Loser:
Guessing right gets you a 19.7% chance to win, and guessing wrong gets you a 7.7% chance to win, for a win rate of 13.7% in the 20% of cases it matters.
Given that these scenarios overall are only 20% of games, we can see that it the difference is just over 0.2% to the overall win rate. But it's better in this case to predict a bad card than the one you're looking for, since two looks at the better deck has a bigger impact than the flipside one look, even though the chances of guessing right are very small.
Other scenarios get more complicated, and I don't want to go in to that kind of depth. The long and short of it seems to be:
- The better the position you're in, the more likely you are to want to name a good card, so that you're improving how bad the worst-case scenario is
- The worse the position you're in, the more likely you are to want to name a bad card, to maximize your best case scenario
- The bigger your deck tends to be, especially relative to the number of cards you'd be happy to draw, the more you want to probably name the bad card
- Naming a good card is likely to be best mostly in cases where something like half your deck (or, especially, more than this) is a good draw.
- Mostly the differences are going to be tiny unless your deck is tiny, which... shouldn't come up very much. The most likely case for this is probably if you're playing against some kind of mill deck(?). A farfetched situation that might actually arise is some kind of doomsday deck where you need to fetch a land out of the doomsday pile. I would love to see that happen, but I'm not holding my breath
