This game is played in bars in Wisconsin, USA, but I'm sure variations are played many places around the world. The game has practical value, since once mathematicians figure out the best strategy, we can probably get free drinks for life!
You are playing a game against the bartender and your $N$ friends for a prize (usually shots of some sort of alcohol). Whoever loses must buy for the whole group, including the bartender. If the bartender is the loser, the house buys.
(Example can also be found at http://www.thedrinkingsurvey.com/bar-dice-drinking-game.php)
Players sit in a circle. Each round, everyone gets a turn. The first person who shakes is ‘setting the score’. All remaining players try to set a new ‘high score’. The person with the high score wins the round and sits out of all remaining rounds.
The first person to shake for the round shakes 5 dice, and has up to three rolls to set a high score. Each player thereafter must try to set a higher score in the same number of rolls or less.
$\cdot$ 1 ’s are wild, and in order for your hand to count at all, it must contain a 1.
$\cdot$ All scoring is pair based: 5 of a kind beats 4 of a kind; 4 of a kind beats 3 of a kind; and 3 of a kind beats 2 of a kind.
$\cdot$ Scoring is also value based; three 5s beats three 4s, and so on.
$\cdot$ Scoring is also turn based; three 5s in two rolls beats three 5s in three rolls.
$\cdot$ After each roll, you are allowed to keep aside dice that you do not wish to re-shake for the remaining rolls.
Once there are two players left, they play a “best of three” match. The first person to lose 2 games is the loser and must pay for everyone.
Finally, whoever had the worst score in the previous round rolls first in the next round.
What is the best strategy to play this game?