Friday 24 November 2017

Greedy Santa

With Christmas approaching, there will be a lot of work parties and opportunities for gift giving. I've already had one such get together, and at this I was introduced to "White Elephant Secret Santa", which is an alternative to the basic 'Secret Santa' that most people know about.
This got me thinking about a 'Game Theory' version of the game, and what the 'best' strategies are.
Firstly some rules:

  1. There are N players
  2. Each players pays N/2 dollars to take part
  3. N envelopes are filled with an amount of money starting with $0, then $1 up to $N-1
  4. Each player takes a number at random, lowest number choosing and opening the first envelope, revealing the money inside.
  5. Subsequent players (starting at 2) can either steal money from another player, or chose to open a sealed envelope.
  6. If a player has money stolen from them, they then get the same option (steal or open). Once a player opens an envelope, this turn ends and a new one starts with the next player
  7. An amount can only be stolen once per turn, and there is a limit on the number of times an amount can be stolen overall (usually the third owner keeps it for good).

The addition of Rule 7 adds an extra level of strategy, as trying to steal the largest amount runs the risk of having it 'frozen' by another player. On the other hand, the last player may have the most power, as they have the greatest choice of what to take (and essentially a retaliation proof grab).
I don't know if anyone has done the maths on this, but it looks as though it may be an interesting programming exercise, both to simulate the game, and to try and generate the best strategy.

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