Taking this into account would make the game much more complicated, because it can introduce an element of bluff.
For a simple example, imagine that there are only 5 characters. On your first turn you know the opponent doesn't have the same card as you, so you've got 4 options remaining. You'd like to ask a question that splits them into 2+2, but if you do this then the card you're holding will make one of the groups into a 3. Your opponent will know that your card is one of the 3, so you've effectively given them a head start. Instead you might sometimes want to split the options 3+2 with your card in the 2, as a bluff.
How often you want to do this must be described by some Nash equilibrium probabilities. It would be interesting to set up a linear programming solver to find these exactly, but so far I haven't had time to set this up. I don't know if it would be practical to solve the full version of the game with 24 characters.
Doesn’t that strategy only work in games like Clue, where everyone is trying to uncover the same hidden character?
In Guess Who, you’re identifying your opponent’s character, not a shared one, so any misdirection only hurts you … because it doesn’t generate extra signal for your opponent, so there’s no strategic benefit to misleading them.
When you are behind the optimal play is to make a gamble, which most likely will make you even worse. From the naive winning side it seems the loser is just doing a stupid strategy of not following the optimal dichotomy strategy, and therefore that's why they are losing. But in fact they are a "player" doing not only their best, but the best that can be done.
The infinite sum of ever smaller probabilities like in Zeno's paradox, converge towards a finite value. The inevitable is a large fraction of the time, you are playing catch-up and will never escape.
You are losing, playing optimally, but slowly realising the probabilities that you are a loser as evidence by the score which will most likely go down even more next round. Most likely the entire future is an endless sequence of more and more desperate looking losing bets, just hoping to strike it once that will most likely never comes.
In economics such things are called "traps", for example the poverty trap exhibits similar mechanics. Where even though you display incredible ingenuity by playing the optimal game strategy, most of the time you will never escape, and you will need to take even more desperate measures in the future. That's separating the wheat from the chaff from the chaff's perspective or how you make good villains : because like Bane in Batman there are some times (the probability is slim but finite) where the gamble pays off once and you escape the hell hole you were born in and become legend.
If you don't play this optimal strategy you will lose slower but even more surely. The optimal strategy is to bet just enough to go from your current situation to the winning side. It's also important not to overshoot : this is not always taking moonshots, but betting just enough to escape the hole, because once out, the probabilities plays in your favor.
abetusk•2mo ago
For example, let's say it's the last turn and your opponent is about to win. Say you may have 2 options but your opponent has 4 options. Instead of whittling it down to 2 options, it's better to guess one of the four. How outrageous should your guesses be is the content of the result and paper.
Paper is on archive (and linked from the video):
https://arxiv.org/abs/1509.03327
gregdeon•2mo ago
ironSkillet•2mo ago
gregdeon•2mo ago
baobun•2mo ago
This could be made more complicated/interesting if you play a series of games and are awarded points based on either how many rounds it took to win or how many remaining cards you still had.
IncreasePosts•2mo ago
Supermancho•2mo ago
I have always asserted that some games (like Heroes of the Storm) suffer from not having catch up mechanics beyond player skill. This is problematic, when player skill can be quantized to an average value that has led to the losing state. This makes it much less likely to ever be a useful catchup mechanic, in comparison to some intrinsic gamble mechanics.
The lack of catch up mechanics also means the games are less interesting because risks are only worth taking after the known state, not casually during as a chaotic factor that might be capitalized on.
gregdeon•2mo ago
sgerenser•2mo ago
abetusk•2mo ago
If you have 100 options available to you, the maximum information gain is if you eliminate half. So, if you can, you always want to employ that strategy.
The problem comes with when you're losing, you might get maximum entropy gain by eliminating half but, because of finite effects of the game ending, that might not matter.
Take the example I gave: the next move you lose and you have 4 options to choose from. Eliminating half (2 in this case) will give you maximum entropy gain but guarantee a loss, since you're not whittling down the remaining list to 1 option. Better to take the hit on entropy in order to at least have a chance at winning.
I don't claim to have deep knowledge but this seems like finite size scaling effects. There's a kind of "continuum limit" of these processes but when you get to actual real-world/finite instances, there are issues "at the edges", where the continuum becomes finite. The finite size of the problems creates a kind of non-linear issue at the edges. All this is very hand-waivy, so don't take it too seriously but that's the intuition I have, at least.
thaumasiotes•2mo ago
Say you're in a game to 500 points and you're losing 460 to 480. There are 13 tricks and a trick is worth 10 points if you bid it.
The other team bids 5 tricks. Assuming they can make this (very safe) bid, they will have 530 points. You are collectively good for about 6 tricks. What should you bid?
If you bid reflecting your hand, you'll score 60 points and lose the game 520 to 530. You could go higher; you can take 8 tricks without even needing to set the other team. That would convert your loss into a win. But it's extremely unlikely that you'll be able to make those 8 tricks.
If you're playing duplicates and getting scored based on how good your result was compared to other teams playing the same hand, you should bid 6. If you're playing this as a one-off and getting scored based on whether you win or lose, you should bid 8 despite the fact that you can't make 8.
This becomes a manners issue in some games where your bid is an important input into later players' bids.
aidenn0•2mo ago
Yes, I learned bridge playing duplicate where preemptive bids[1] are totally fine, but at some rubber bridge tables you won't get invited back if you have a habit of bidding them.
1: https://en.wikipedia.org/wiki/Preempt
thaumasiotes•2mo ago
There's no advantage to winning immediately. You aren't scored on time taken.
So, it's better to use the better strategy.
SatvikBeri•2mo ago
But (1/2, 1/2) is clearly a better choice than just guessing a specific individual. So it must be the best choice.
gregdeon•2mo ago
chrismorgan•2mo ago
Or lose. Last month I played Guess Who with my Indian wife who hadn’t encountered it before, and in a couple of rounds she made mistakes in eliminating tiles, so that my wild guess saved her from losing to her own incorrect final guess.