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Mia

This is a very old and ancient, bluffing dice game, played with two dice and a flat bottomed container with a lid, for any number of players.

## Play:

All players start the game with three lives. The first player rolls the dice without revealing what was rolled. This initial player then has three choices of what to announce to the others:

• Announce truthfully what has been rolled,
• Announce (by lying) a greater value than that rolled.
• Announce (by lying) a lesser value than that rolled.

The dice values are ranked by multiplying the higher value of the two by 10 and adding the lower value to produce a two digit number.

All possible results are ranked in order as follows: 21, 11, 22, 33, 44, 55, 66, 65, 64, 63, 62, 61, 54, 53, 52, 51, 43, 42, 41, 32, 31

The highest roll, 21 (called Mia) is followed by all the doubles ranking from 11 up to 66, and then subsequently ranked as the highest two digit number.

After the initial player has announced their call, the dice are passed to the next player without revealing the values thrown. This player now has three choices:

• Believe the caller and roll the dice again in an attempt to roll something better.
• Call the last caller a liar and look at the dice.  passer loses a life. However, if the dice show a greater or equal value, the challenger loses a life.
• Pass the dice to the next player without looking at them, relieving the original caller of any forfeit of lives, and taking responsibility for the call himself.

Players must either announce a greater value than the previous one called or pass the dice without looking and take responsibility for the current called value.

Should the dice be passed all the way back to the original caller of a throw, that player must  choose one of the following two options:

• Call the previous caller a liar.
• Call a higher two digit value, either not rolling or re-rolling the dice.

If Mia (21) is either rolled or announced, then the player who is to lose a life, loses two.

The last player with a life, wins the game.

Before deciding whether to bluff, a player needs some idea of what a "good" roll is, and this is not as simple as it first seems. Since there are two ways to achieve any result that is not a double (e.g. 43 could be 3-4 or 4-3), while doubles can only be made one way, then the "middle" roll in a game is not 62 but 54, regardless of the fact that ten results rank above and below 62, while there are twelve possible results ranked above and eight below the 54. Due to the bias in the structure of the two digit results, relative to possible rolls of two dice (21 results out of 36 possible dice combinations), the likelihood that someone rolling 62 (the numeric median result) will be beaten by a subsequent roll is only about 39%, while a player rolling a 54 (the actual median result) has even odds.

All the possible two digit values, and the percentage chance of each being subsequently beaten with a single roll is as follows:

21 (0%)  "Mia"

11 (5.6%)
22 (8.3%)
33 (11.1%)
44 (13.9%)
55 (16.7%)
66 (19.4%)

65 (22.2%)
64 (27.8%)
63 (33.3%)
62 (38.9%)
61 (44.4%)
54 (50%)
53 (55.6%)
52 (61.1%)
51 (66.7%)
43 (72.2%)
42 (77.8%)
41 (83.3%)
32 (88.9%)
31 (94.4%)