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An implementation of a dice bluffing game, similar to Liar's Dice. A player, the 'Declarer' rolls the dice and announces what poker hand is under the cup. The player to the left, the 'Caller', announces whether he or she believes the Declarer. If the Caller believes the Declarer then the Caller takes the cups and is the new declarer, and must declare a higher poker hand from the dice under the. Liar’s dice poker, or lying, is one of the most famous dice poker games that exist in Spain. It is inspired by the English deck of cards, with the main cards -or the most valuable cards in poker.
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.
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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 | |||
|---|---|---|---|---|
| 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 | |||||||
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
Posted on 2017-02-10 | Comments (0)
Liar’s Poker recasts the bluffing spirit of the game of poker into an I Doubt It-style affair, doing away with the gambling aspect altogether. That makes it an excellent game for younger players, or to familiarize new players with the poker hands. It can be played with two to eight players, but is best with three to five.
Object of Liar’s Poker
The object of Liar’s Poker is to successfully determine whether the active player in fact has the hand they claim to have.
Setup
Liar’s Poker is played with a 54-card deck of playing cards, formed by adding two jokers to a standard 52-card deck. We’d be lying if we said we didn’t wish you’d use Denexa 100% Plastic Playing Cards in your game. You’ll also need something to keep score with. Pencil and paper is fine, but it’s much simpler to use a supply of markers, such as poker chips.
Select the first active player by any convenient means, such as mutual agreement or high-card draw. Shuffle and deal five cards to that player only. The rest of the deck becomes the stock.
Game play
The first player looks at the five-card hand they have dealt. They then declare any standard poker hand that they assert the hand contains (jokers act as wild cards). They may simply declare the hand type that they purport to hold (e.g. “a pair”), or they may declare more specifics, such as “a pair of 10s”, “a pair of 10s with an ace kicker”, etc. The player to the left of the active player must decide whether or not they believe the declaration. If they do, they accept the hand, and the cards pass to that player.
The new active player then looks at the cards. They don’t reveal whether or not the declaration was true or not. Instead, they may discard up to four cards, face down, and draw new ones to bring the hand back up to five cards. They must then make a declaration higher than that of their predecessor. This may be a wholesale improvement in the hand (e.g. going from “a pair” to “two pair” or “a pair of 5s” to “a pair of 9s”) or it may disclose more information than the previous one. For example, if the previous player declared “a pair of jacks”, then “a pair of jacks with a queen kicker”, “a pair of jacks with a 7”, etc. would qualify as a higher declaration.
If a player doesn’t believe a declaration that has been presented to them, they call “Liar!” If the declaration was honest, then the active player reveals just as many cards needed to prove the declaration correct, and the doubter is given one point. Otherwise, the cards are discarded, face down, and the liar gets one point. In either case, the cards are shuffled. The player that scored the point is dealt a new hand and becomes the new active player.
Bid Poker Liar Game
Game play continues until one player reaches a predetermined number of points. The player with the lowest score at that point is the winner.
Liar's Poker Summary
Posted in Game Rules | Tags: card games, liar's poker, poker