In the proud tradition of this blog I’m holding a new smallest number tournament. The rules of this wonderful game are as follows:

- Each player chooses an integer greater than zero.
- If more than one player chooses the same number, that number is disqualified.
- The player who played the smallest number that didn’t get disqualified wins.

For example, if Bernie plays 1, Joan plays 2 and Dave plays 5, Bernie wins, because he played the smallest number. But if there had been an extra participant, Frank, who had also played 1, Joan would have won, because 1 would have been disqualified and 2 was the next smallest number played.

But this time I don’t want you to play the game – I want you to write a small program that plays the game. There are two ways to participate in this contest

Firstly, you can write a Python class that has at least the following methods (all of these except play() can just pass):

- announce_num_players(integer): take an integer giving the number of participants in the tournament, don’t return anything
- announce_game_length(integer): take an integer giving the number of rounds that will be played, don’t return anything
- get_ready(): do any final initialization
- announce_result(result): take a list with all the other players’ plays from the most recent round (the same player will always occupy the same place in this list)
- play(): return your number for the round

An example minimal contestant could look like this:

class Player: def __init__(self, number = 4): self.always_play_this_number = number def get_ready(self): pass def announce_num_players(self, num): pass def announce_game_length(self, num): pass def announce_result(self, result): pass def play(self): return self.always_play_this_number |

(Always play 4 unless initialized to always play something else, and don’t do anything with the extra information.)

Secondly, you can come up with a distribution. It can be a constant distribution, with constant probabilities for each number, like this:

[0.3, 0.3, 0.3, 0.1] |

(play numbers 1-3 with a probability of 30% each and number 4 with a probability of 10%)

or a list comprehension that uses information about the number of players and rounds, like this:

[1.0/num_players for x in range(num_players)] |

(play numbers up to the number of players with equal probability)

or any other convenient-to-me way of describing a distribution in list form.

Submissions are open until I’m satisfied that most people I know who might be interested have had time to come up with a submission. I will be happy to help with the programming if you’d like. I will be participating myself, but I promise I will not use information from other submissions.

Send submissions to my email address which should be visible in the side panel, preferably with a subject like “Smallest number challenge”.

The prize is the joy of participation, and it will be given to all participants!

**Details about the tournament arrangements**

I will score each tournament in at least two ways: the official way and Vadim’s zero-sum way.

- In the official scoring, a player who plays a winning move receives one point. A player who doesn’t play a winning move receives zero points.
- In Vadim’s zero-sum scoring for n-player tournaments, the winner gets n-1 points, losers get -1 point, and if there’s no winner, everyone gets 0 points.

I will run several tournaments with varying numbers of rounds, all with the full complement of participating players.

The tournament-running program will always call announce_game_length() and announce_num_players() for each player before a tournament starts, and announce_result() every time a round has been completed. Players that support the special value None as an argument from these functions will participate in a special tournament where the players don’t get this information.

I’m in. Might take some time though.

Vadim

How are points counted? 1 point for win and 0 for non-win or something else like -1 for losing etc?

vadim

I’d be a zero-sum game for instance by giving the winner n-1 points, losers -1 and in case of a draw everyone gets 0. Where n is the nr of the players.

vadim

when you run a tournament, are the algorithms given the number of rounds in advance?

vadim

I’ll add some details. Why do you like the zero-sum system? Sounds to me like the wins become too valuable with a large number of players.

Yeah, the API functions for announcing game length, number of players and previous results will be called whenever appropriate.

sam

zero-sum because even if you dont make it zero-sum, I will have to subtract other’s wins from my utility function in order to achieve “best score among players” and not just “as best score as possible no matter how others do”.

vadim