# Planet of Lies - Number Game

• CharmedQuark
DaveE that there is no optimal strategy to guarantee a win in this game. Since all players have the same options to choose from, there will always be a draw. However, it may be possible to increase the chances of winning by studying previous games and analyzing the number patterns. In summary, the number game described in the conversation is played by five players for ten rounds. The player with the highest unmatched number in each round wins points equal to their number. There is no optimal strategy to guarantee a win, but analyzing previous games may increase the chances of winning.

#### CharmedQuark

So after reading the planet of lies thread I thought it would be interesting to figure out the optimal way to play the number game described. It is played as follows:

There are five players and ten rounds. During each round every player picks a number between 1 and 5, This choice is secret, no player knows what the others picked. After all players have chosen the numbers are revealed. The player with the highest unmatched number wins the round and is awarded points equal to his number. A number if matched if another player has written the same number i.e if 5, 5, 5, 4, 3 were written then 4 would win since the fives are matched. The points are added each round and after ten rounds the player with the most points wins.

So is there an optimal strategy to guarantee a win? If not is there a certain strategy where the probability of winning is >50%, and finally if this cannot be achieved is there a strategy which guarantees a draw?

CharmedQuark said:
So is there an optimal strategy to guarantee a win?

Nope. Imagine that each player is playing with the same strategy-- since there are no differing inputs available to any player, each player will always select the same number, and there will always be a draw.

My wife actually used to play a similar game online that was done in a weekly giveaway-- the rules were that each person would submit 3 integers, each 1 or greater. Then, at the end of the week, the person that had submitted the LOWEST unmatched integer would win a prize.

From week to week, I think the lowest number we ever saw was something like 59. And sometimes the winning number was in the 250+ ballpark. We tossed around various ideas about how to maximize the chances of winning, but really we couldn't come up with anything mathematical. The only good way we figured you could strategize was to know how many people were entering, and have some good statistics on previous games that were played.

DaveE

davee123 said:
Nope. Imagine that each player is playing with the same strategy-- since there are no differing inputs available to any player, each player will always select the same number, and there will always be a draw.

I agree