Liar's Poker

[dogdrool]

Can somebody please summarize the rules of Liar's Poker? (The kind played with dollar bills). I've found the page on the wizard of odds, but I'm still confused on the details. Also, some people at work play with wild cards.

Essentially, I'm looking for the most detailed explanation of Liar's Poker that's out there.

[MarkGritter]

(I find Liar's dice to be somewhat easier to understand, and there are a lot of explanations out there since it appared in Pirates of the Caribbean 2... it's basically the same game.)

Each player has a bill whose serial number is known to him but not to the other players. You are bidding on how many of a given digit there are on all the bills combined.

When it is your turn, you must either make a bid higher than the previous bid, or challenge the last bid. A bid is higher than the previous one if it either has a higher number of digits, or the same number but a higher digit. (Typically for liar's poker the order of the digits is 2345678901, so that 1's are "aces".)

For example, an opening bid might be "3 threes". The next play could bid "3 fours" or "4 twos" to beat this, or jump to something like "5 nines".

When there are no more bids (everybody but the last bidder has challenged), the bills are revealed. If the last bidder was correct, he collects money from all the other players; if he was incorrect he pays out. This is easy to understand for just two players. With multiple players you can have a situation where player A bids, player B challenges, but then player C ups the bid--- there is no showdown yet and player A may re-bid or challenge, and player B must act again as well.

The bid does not have to be exact. If the last bid was "5 sixes" and there are actually 8 sixes, the bid still wins.

You need to be clear on the variant before starting--- some players use 0-9, or wilds, or other crazy variants such as poker rankings (straights and full houses instead of just number of digits).


Incidentally, Liar's poker is a great game for online chat or other forums because you can verify your opponents' digits by getting secure hashes from them ahead of time.

For example, using this web page: http://www.johnmaguire.us/tools/hashcalc/

I would first reveal that my SHA-1 hash is:
<font class="small">Code:</font><hr /><pre>
b0bfe6d60756e02c00e0aaad5e0560e4490c6b24
</pre><hr />

Then we could play the game, and when it was time for showdown I would reveal that the string is:
<font class="small">Code:</font><hr /><pre>
My digits are 20767189.
</pre><hr />
which the other players could then verify using the calculator.

As long as the hash is secure, the player will not be able to change his digits after the game has started. As long as the player includes a "salt" (some text in addition to "My digits are" which is not predictable), his opponents will not be able to figure out the digits from the secure hash. (If you don't use a salt I could just have a dictionary of all 100 million hashes for all possible digit strings.)

I'm sure somebody must have studied Liar's dice or Liar's poker from a game-theoretical standpoint but I haven't yet found any references.

[Phat Mack]

There are different rules in different localities, but Mr. Gritter's explanation is excellent for the basic game.

At one time, when there were mistakes in printing, the Treasury would reprint runs of $1 bills with an asterisk in front of the serial number. Some people played that these asterisks were wild. Others play that the 2s are wild. I've never played with wild cards.

Other variations:

--If there are NO occurrences of the rank bid, then the bidder wins.

--After the bid has been called down by all players, some play that the bidder has the right to re-open the bidding. Some feel that this rule protects fish, but I think it punishes them and rewards the skillful player.

At one time the GBC published a book on this game by John Archer that was pretty good. they may still have some copies.

[dogdrool]

MarkGritter, that is a very fine response. Thank you. Phat Mack, I'll look for the John Archer book.

Why is there no notion of raising in Liar's Poker. Do some variants have it?

[Phat Mack]

Why is there no notion of raising in Liar's Poker. Do some variants have it?

Probably because it isn't really a vying game in the sense that nobody has a hand that they believe is stronger than their opponent's. Instead, they have a communal hand and they are betting on their guesses as to what it is.

(The bridge bid of 'double' (and even of doubling for take-out) might make sense as a liar's poker variant.)

Liar's Poker: A Winning Strategy