Perudo

Basically the game liar's dice from Pirates of the Caribbean.  Except you aren't giving this man your soul when you lose:

Do you fear dice?

My friends hate it when I play this game.  Because I think too much, and it's a drinking game.  But the whole concept of the game is fascinating.  There's a total of 5 dice per player (so with 5 players, you start with 25), only 5 of which you know.  You have to guess with strictly increasing bets how many dice there are with a certain number or a one.  Therefore a bet of three threes means that you think that under all the cups, there are at least either three threes, three ones, or a pleasant combination of the two.  An average roll at the beginning of the game will net you about 8 each of two's and one's, three's and one's, four's and one's, etc.  But the whole idea is to use your dice in order to give yourself an advantage: there's a lot more chance for your five dice to roll abnormally than the other 20 to roll abnormally.

The betting system is thus: each subsequent bet must either increase the number of dice with a certain number OR increase the number on the dice but keep the same number of dice.  So if I say there are four threes, then a legal bet would be either five threes or four fours.  However, 2 threes is right out.

And he shall snuff it....

 After each bet, the next player can call bullshit, bologna, liar, scurvy dog, or some other appropriate (or inappropriate) phrase.  If he does not, then he must make a bet.  If bullshit is called, all dice are revealed.  The loser removes one of his/her die, and the game continues.

Ones are special.  The initial bet must halve the number of dice bet previously (rounding up).  After ones are started, there are two separate betting tracks, one for ones and one for everything else.  They do not affect each other.

Now the trick of the game, after playing several times, is to force an opponent to make a bet which is just completely awful and ludicrous.  This means that if I am holding five of one side in my cup, I'm betting high just so the betting doesn't make it all the way back to me.  It should go without saying that the more dice you have, the better advantage you have.

 The second trick is to recognize when someone has you beat and you need to analyze your options.  Picture this: there are three dice left.  Two fours are bet by your opponent.  You're looking at a three in your cup.  There are a couple bets you might consider.

1.  Bullshit.  Think about your opponent.  The probability that they have two fours (or two ones, or some combination) under their cup is 1/9.  This is not as simple as it seems.  The probability of rolling "doubles" is 17/36, or just under 1/2.  Does your opponent seem like the lying type?  If so you're in luck.  Does he seem like the play it safe type?  Well then maybe you want to choose another option.

2. Three fours.  You're only putting your opponent into a pickle if he actually *has* two fours.  I hope you're a good liar if you choose this one.

3. Three threes.  You already know there's one.  So of the two unknowns, both have to be threes.  1/9 probability of winning.

4.  One one.  Either there's a one on his first die or a one on the second.  1/6+1/6.  1/3.

Here, bullshit might be your best option, depending on who you're playing.  A lot of times when I'm starting out rounds with 10 or fewer dice I just spout out "One [insert random number here]."  Second best option is clearly one one.

Now the challenge here is to be able to do this in your head.  While drinking.  Do it.

Make your friends some of these so they are placated while you think.