Liar's Poker Rules Dollar Bills

21 years after publication, Liar's Poker feels both relevant and ancient. Relevant because it seems the Big Swinging Dicks of Wall Street are ever with us; ancient because of references to things like WATS lines and the lionizing of Salomon Brothers trader John Meriwether, whose Long-Term Capital Management would spectacularly implode in 1998, and Michael Milken, who apparently had not yet. Wall Street's biggest banks could be broken up by the U.S. Congress in the coming year in an eventual reckoning over the financial meltdown of 2008, 'Liar's Poker' author Michael Lewis said on. 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. The dollar game can be played by people of all ages. There's no skill involved, and there's no thinking about what move to make. Reading the numbers revealed on the roll of the dice and following the rules of play are all you need to do to either increase the pile of money in front of you or lose it all.

Having finished Liar's Poker: Rising Through the Wreckage on Wall Street by Michael Lewis, last week, it seemed appropriate to explain the rules of the game. Yes, a review might have been interesting, but definitely not more entertaining (and I would consider the book an entertaining read). So, in the spirit of trading sites everywhere, I have written this tutorial to explain the basics of liar's poker:
1) There are several version of liar's poker. One involving bidding and another more in the spirit of poker. Because the bidding version appears to be the most popular, and because Micahel Lewis features it in his book, I will discuss the general rules for that game. 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 center of the group. Shuffle the bills.
4) Have each player take a bill. Do not show it to any other players. Keep your 'hand' covered, just like in a game of cards.
5) Look at your serial number. In general, 1's count as aces and 0's count as tens, but make sure to clarify this at the beginning of the game. Some versions play with 0 being the lowest number and 9 being the highest. Either way works out well. Count the number of times each number appears in your serial number. This is your hand. Remember it.
6) Begin the bidding. You can choose the starting player in any number of ways. If you have only two players, a coin toss works well. Otherwise, rolling dice or picking a card. Use your imagination.
7) Make a bid. That means, make a bet on how many of a certain number you believe to be among all the serial numbers. Say you have 2 5's on your serial number. You could safely bid 2 fives, as you know there to be two five's for a fact.
8) Continue to the next person. This person can now bid a higher amount of the number you last bid on, say 3 5's; or, they can bid a higher amount on a lower number, say 4 4's or 4 2's; or, they can bid on any amount of a higher number, say 2 6's or 1 ace.
9) Another option everyone after the first player has is to call the last player's bid a lie, or a bluff. Say you do not think there could possibly be 4 aces among all the serial numbers, but that was the last bid. You could call the last player's bid a bluff.
10) Now, the next person can agree with you and also call that player's bid a bluff. But if they do not believe it to be a bluff, they can also continue the bidding in the manner explained in step 8.
11) If the belief that a person has in fact bluffed becomes the consensus of the entire group, everyone must show their serial numbers.

Liar's Poker Rules Dollar Bills

12) Count up the serial numbers.
13) If the person being called the liar actually bid correctly (e.g. the player said there were 5 aces and there were, or there were more), then that player wins. Each player gives him a dollar, or a point, whichever has been decided upon.
14) If the person is incorrect, then that player must give everyone else a dollar, or a point, whichever is decided upon. You do not have to play for dollars; playing with smaller or larger amounts works just as well.

Liars Poker Rules Dollar Bills Free

To watch a sample game, click here. There are also free tournaments and games on that site. If you are interested in the odds behind the game, I found this page (go to the bottom). It's not perfect, but interesting nonetheless.

Introduction

Rules

1. Liar's Poker is played using randomly picked currency from your wallet. The denomination does not matter. Hoarding ringers is strictly not allowed.
2. 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.
3. 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.
4. A hierarchy of numerals should be established. I prefer zeros are low and nines are high.
5. Players in turn bid on the combined numbers in all serial numbers, your own and those of the other players.
6. Each player must in turn either declare a higher hand than the player player or challenge.
7. In a 3+ player game all players must challenge to end the game.
8. 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.
9. 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

Liar S Poker Rules Dollar Bill

Number of Numerals	Number of Other Players
	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.	4 o.a.k.	3 o.a.k.	2 o.a.k.	1 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

o.a.k. = 'of a kind'
The next table summarizes the table above in groups of the more frequent occurrence of any digit.

Greatest Frequency Odds in Liar's Poker

Greatest Frequency	Probability
8 of a kind	0.0000001
7 of a kind	0.0000072
6 of a kind	0.0002268
5 of a kind	0.0040824
4 of a kind	0.0458955
3 of a kind	0.3124800
2 of a kind	0.6191640
1 of a kind	0.0181440
Total	1.0000000

Written by:Michael Shackleford