6 players sitting in a circle and each assigned a card among 2 Hearts, 3 Hearts, ..., Ace Hearts (i.e. any of the Hearts cards). Holding her card above his forehead (i.e. Indian Poker fashion), each of them can see everyone else's cards, but not her own.
Round 1: Starting from player 1 and going clockwise until player 6, they take turn to call out their best guesses of what is their respective order among themselves (i.e. am I largest, or 2nd largest, etc.).
Round 2: Starting from player 6 and going counter-clockwise until player 1, they take turn to call out their best guesses of their respective order and the number on their respective card.
Objective: To maximise, as a group, the number of people who announced correctly in round 2.
- At any point in time, player's calls can incorporate any information that has been provided thus far.
- If it matters, the group is only told whether each call in round 2 is correct or incorrect at the end of the round, not immediately after calling.
- Technically, in rounds 1 and 2, the rule does not forbid calling out other integers that might convey more useful information (as long as they are in the allowable range for the order and card values).
- Players may discuss their strategies prior to distribution of the cards.
Find a strategy for the players that maximizes the expected score. What happens if we generalise to $n$ players with card values $1,\dots,m$?