w**9
发帖数: 225 | 1 Todd explains the rules of this game:
1. You can take as much time as you need and use any help other than asking
Todd...
Once you sit down to play, no shenanigans!
2. Todd will then take the deck of cards and a normal (fair) die and
secretly roll the die and pull a card from the deck whose suit matches: 1-2
= Spades, 3-4 = Hearts, 5-6 = Diamonds.
3. Todd then passes this card, face down, to Emily and repeats the process
for Charles, Doug and Fran.
4. Each player puts the card on their forehead so that they know what
everyone else has but not what they have.
5. Simultaneously, each player announces one of the three card suits or says
, "Pass".
Outcome:
If everyone says, "Pass", you lose. If anyone says a suit other than what
they have on their head, you lose. If at least one person guesses their card
and no one guesses wrong, all four people win.
Todd explains the simplest approach: "Getting a 1/3rd chance of winning is
pretty easy; just have Emily guess, 'Spades' and everyone else says, 'Pass'."
Can you do better? | g******2
发帖数: 234 | 2 you can induce from 2 people situation:
Suppose you have A & B, a better strategy is that A say "Pass" when B is "
Spade", other wise say "Spade". In this case your winning chance is 1/3*2/3+
1/3=5/9.
3 people situation：
A say "Pass" if B or C is "Spade", B say "Pass" is C is "Spade", otherwise
say "Spade". In this case your winning chance is 1/3*(2/3*2/3) + 1-(2/3*2/3)
=19/27
By induction, it should be 1/3*(2/3)^(k-1)+1-(2/3)^(k-1)=1-(2/3)^k |
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