Liar's Poker Rules Dollar Bills

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A serial number on a five dollar bill

Liar's poker is an American bar game that combines statistical reasoning with bluffing, and is played with the eight digits of the serial number on U.S. dollar bills. The digits are usually ranked with the 1 as 'ace' as the highest value, followed by 0 as '10', down to 2 as the lowest. Each player holds one bill, unseen by the other players. The objective is to guess how often a particular digit appears among all the bills held by all the players. Each guess or bid must be higher in quantity, or equal in quantity but higher in value, than the previous bid. The round ends when all the other players challenge a bid.

The game is similar in structure to Liar's dice.

Gameplay[edit]

They're playing Liar's Poker, a sort of poker played with money bills instead of cards. Liar's poker is an American bar game that combines statistical reasoning with bluffing, and is played with the eight digits of the serial numbers on a U.S. The numbers are usually ranked with a zero counting as a ten, and a 1 being highest as 'ace'.
As with any game, remember to clarify rules before beginning since more than a single version of the game likely exists. 2) The game requires 2 or more players and each player needs a dollar bill (several if you want to increase the uncertainty of serial numbers drawn). 3) Put all bills face down, covering the serial number, into a pile in the.

Usually the game is played with random bills obtained from the cash register. Each player takes a dollar bill and looks at its serial number without letting any other players see it. The starting player makes an opening bid on how many of a particular digit appears across all serial numbers held by the group. For example, if the first player bids three 6s, he is predicting there are at least three 6s among all the players including himself. The next player can bid a higher number at that level (three 7s), any number at a higher level (four 5s), or challenge the bid. The game continues clockwise around the table until a particular bid is challenged by every other player. If the challenge is correct, and the total number of the digit on all the bills is lower than the bid, the bidder loses a dollar to each of the other players. If the challenge is incorrect, the bidder wins a dollar from each player.

In popular culture[edit]

In the 1965 film Cat Ballou, the sheriff is confronted playing liar's poker at the barn dance.
In the 1972 film The Getaway, Steve McQueen’s character Doc McCoy challenges Ali MacGraw’s character to a game while looking at a bill, by saying 'Five fours'.
Elliott Gould's and Jim Bouton's characters play a round as friends in the beginning of the 1973 neo noir film, The Long Goodbye.
In the 1977 movie Semi-Tough, Burt Reynolds' and Jill Clayburgh's characters play an ongoing game of liar's poker.
Characters on the show Quincy M.E. were often seen playing Liar's poker.
In the WKRP in Cincinnati episode 'Herb's Dad', Herb's father, and later Herb himself, play liar's poker with Johnny and Venus.
In Season 3, episode 8 of Magnum, P.I., 'Foiled Again,' Magnum and his two friends pass the time by playing liar's poker.
In his 1989 book Liar's Poker, Michael Lewis details how Salomon Brothers traders would play liar's poker. He recounts how John Meriwether was once challenged by CEO John Gutfreund to a game of liar's poker for stakes of one million dollars and then declined to play when confronted by a counter-offer of ten million from Meriwether.
A game of liar's poker was played in an episode of the TV series Hustle (Season 3, Episode 3) where one of the main characters plays and loses against two merchant bankers.
In The Wire episode 'Dead Soldiers', Tommy Carcetti and Anthony Gray play a game.
In the 2011 movie Hall Pass, the group of characters play a game.
Anne O Faulk's novel Holding Out uses the game as a plot point.
In John D. MacDonald's novel, A Tan and Sandy Silence, Travis McGee and Meyer play the game to determine who will pay for dinner and drinks.
In Paper Lion by George Plimpton the coaches play at a bar after practice at training camp.

Literature[edit]

Liar's Poker by Michael Lewis

References[edit]

Retrieved from 'https://en.wikipedia.org/w/index.php?title=Liar%27s_poker&oldid=982762583'

Introduction

Rules

Liar's Poker is played using randomly picked currency from your wallet. The denomination does not matter. Hoarding ringers is strictly not allowed.
All players must agree on the stakes, for example $1 per person per round. You do not have to use the exact bill you are playing for, for example you can use a $20 bill although playing for only $1.
A rule should be set for who goes first, for example whose letter in the serial number is lowest, or who won the last time. Who goes first is not very important, in my opinion.
A hierarchy of numerals should be established. I prefer zeros are low and nines are high.
Players in turn bid on the combined numbers in all serial numbers, your own and those of the other players.
Each player must in turn either declare a higher hand than the player player or challenge.
In a 3+ player game all players must challenge to end the game.
Eventually a player will be challenged. Then the combined serial numbers will be used to determine if the last hand called exists. For example if the challenged hand is four eights then there must be at least four eights on all serial numbers. If players trust each other than can simply declare how many of the given number they have, of course the challenged player reserves the right to see the bills if he so requests.
If the serial numbers support the challenged player then the player will win the agreed upon stakes from each other player. Otherwise the challenged player must pay each other player the agreed upon stakes.

Let's look an example. Suppose there are three players playing for $1 stakes with the following serial numbers:

Player 1: 06742088
Player 2: 92859819
Player 3: 07202503

Here is the play of the game, player 1 goes first:

Player 1: 2 zeros
Player 2: 2 fives
Player 3: 3 zeros
Player 1: 3 eights
Player 2: 3 nines
Player 3: 4 zeros
Player 1: 5 zeros
Player 2: challenge
Player 3: 6 zeros
Player 1: challenge
Player 2: challenge

At this point there must be 6 zeros for player 3 to win. There are only 5 so player 3 must play player 1 and 2 $1 each. Had player 2 had a zero then player 3 would have won.

Strategy

In 3+ player games it often happens that a player is in a damned if you do damned if you don't situation. Assuming that by challenging you will definitely lose, and by raising you definitely will be challenged, you should always raise in a 2-player game, raise if your probably of winning by doing is 25% or greater in a 3-player game, 33.33% in a 4-player game, and (n-2)/(2n-2) for n players. Of course nothing is ever certain, so this scenario is admitedly unrealistic.

It often happens that you need at least one other player to have at least one of a certain number for you to win. Assuming nothing about the other player's numbers (again an admitedly unrealistic assumption) the following table shows the probability of the total number of any given number according to the number of other players.

Probabilities in Liars Poker

Number of Numerals	Number of Other Players
Number of Numerals	1	2	3	4
0	0.430467	0.185302	0.079766	0.034337
1	0.382638	0.329426	0.212711	0.122087
2	0.148803	0.274522	0.271797	0.21026
3	0.033067	0.142344	0.221464	0.233622
4	0.004593	0.051402	0.129187	0.188196

So if you are playing with two other players and you have 3 fives and call four fives the probability of winning if you are challenged is 1-0.185302 = 0.814698. However if you need two fives the probability drops to 1-0.185302-0.329426 = 0.485272.

The next table shows the probability that any specific number will appear n times.

Specific Number Odds in Liar's Poker

Number	Probability
8	0.00000001
7	0.00000072
6	0.00002268
5	0.00040824
4	0.00459270
3	0.03306744
2	0.14880348
1	0.38263752
0	0.43046721
Total	1.00000000

The next table shows the probability of every possible type of bill, categorized by the number of each n-of-a-kind. For example, the serial number 66847680 would have one three of a kind, one pair, and three singletons, for a probability of 0.1693440.

General Probabilities in Liar's Poker

8 o.a.k.	7 o.a.k.	6 o.a.k.	5 o.a.k.	Probability
1	0.0000001
1	1	0.0000072
1	1	0.0000252
1	2	0.0002016
1	1	0.0000504
1	1	1	0.0012096
1	3	0.0028224
2	0.0000315
1	1	1	0.0020160
1	2	0.0015120
1	1	2	0.0211680
1	4	0.0211680
2	1	0.0020160
2	2	0.0141120
1	2	1	0.0423360
1	1	3	0.1693440
1	5	0.0846720
4	0.0052920
3	2	0.1270080
2	4	0.3175200
1	6	0.1693440
8	0.0181440
Total				1.0000000