Liar's Poker - Example Game

Example Game

If every player follows the exact mathematical formulae, a possible game is the following. Keep in mind that the order of least to most valuable number is 2-3-4-5-6-7-8-9-0-1.

Player 1: 21068274
Player 2: 44789800
Player 3: 27706500
Player 4: 63523655

Player 1 begins

Player 1: 3 twos (has 2 twos - 92% chance others have another two)
Player 2: 4 fours (has 2 fours - 71% chance others have another two fours)
Player 3: 4 zeros (has 3 zeros - 92% chance others have another zero)
Player 4: 5 fives (has 3 fives - 71% chance others have another two fives)
Player 1: Challenge (can only outbid if others have at least 4 more of two, six, seven or eight, which is a chance of 21%, and 21%<33%)
Player 2: 5 zeros (has 2 zeros - 44% chance others have another three zeros)
Player 3: 6 zeros (has 3 zeros - 44% chance others have another three zeros)
Player 4: Challenge (can only outbid if others have at least 4 more fives, which is a chance of 21%, and 21%<33%)
Player 1: Challenge (can only outbid if others have at least 5 more twos, which is a chance of 9%, and 9%<33%)
Player 2: Challenge (can only outbid if others have at least 5 more fours, eights or zeros, which is a chance of 9%, and 9%<33%)

Player 3 has been challenged by all the other players. Each player tells his amounts of zeros. For Player 3 to win, together they have to have at least 6 zeros. They have exactly 6, so Player 3 wins and the other Players have to pay him the agreed amount.

This game was played with four players who fully understood and applied the mathematical formulae, but in Liar's Poker it's about bluffing and trying to influence other players' decisions to your benefit, while keeping these statistics in the back of your mind.