In 2010, I first played Liar's Dice as an in-game gambling activity of the video game Red Dead Redemption. I had never heard of it, but quickly grasped the rules and bidding strategies.
As you can see on BGG, there are endless flavors of Liar's Dice, also known as Perudo, which try to make a "better" version of it, but in my opinion, they add fluff to a game where it isn't needed.
Thus, here are the rules to the basic version of Liar's Dice as played in Red Dead.
Liar's Dice is played several players over the course of a number rounds. Each player starts with 5 dice at the beginning of the game. Each round, one player (technically this could be multiple players, but usually it's only one) will discard one of their dice. When a player discards their 5th dice, they are out of the game. Rounds continue until there is a single player left.
Thus, the goal is to be the final player. In terms of gambling, players simply pay an ante at the beginning of the game and the winner collects the full pot.
All players shake their 5 dice in their cups and slaps them down on the table. They can look at their dice, but should keep them secret. The starting player states the opening bid.
A bid is a statement of how many dice of a given pip-value you think there are under everyone's cups. They are stated in this form: "4 Threes". This means the bidder is stating that there are 4 dice under everyone's cups that are showing 3.
"4 Threes"




"5 Fives"




Think of a bid being prefaced with "At Least...". For example "At Least 4 Threes" or "At Least 5 Fives".
On your turn, you have 3 options:
Most of the time, you'll raise the previous bid. To do this, you must increase either the number of dice or the pip-value or both.
Previous Bid
"4 Threes"
  
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Increase the Number of Dice
"6 Threes"
    
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OR |
Increase the Pip-Value
"4 Fives"
  
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OR Increase Both
"6 Fives"
    
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If you feel the current bid (by the previous player) is too high, you can call a bluff. This ends the round. All players reveal their remaining dice from under cups and the dice that match the bid's pip-value are counted.
- If the number of less than the current bid, then the previous bidder looses one die.
- Otherwise, the player who called the bluff looses one die.
For example, the Previous Bid was "4 Sixes" when Player 2 calls it a bluff.
This means that Player 2 doesn't believe there are at least 4 Sixes under everyone's cup.
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Under Player 1's Cup
 
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Under Player 2's Cup
 
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Thus, there is a total of only 3 Sixes
 
Since there were only 3 Sixes, then Player 2 who called the Bluff (and was wrong) looses a die.
Everyone re-rolls their dice under their cups and the next player starts the next round with a Starting Bid.
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If you feel the previous player's bid is the exactly right, you can call a "Spot-On". This ends the round, too. All players reveal their remaining dice from under cups and the dice that match the bid's pip-value are counted.
- If the number of dice is exact, then all players except for the one who called Spot On looses one die each.
- Otherwise, the player who called Spot On looses one die.
For example, the Previous Bid was "4 Threes" when Player 2 calls "Spot On".
This means that Player 2 believes there are exactly 4 Threes under everyone's cup.
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Under Player 1's Cup

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Under Player 2's Cup
 
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Under Player 3's Cup
 
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Under Player 4's Cup
 
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Thus, there are exactly 4 Threes
  
Since there were exactly 4 Threes, then the bid was Spot On and all players except for Player 2 looses a die.
Everyone re-rolls their dice under their cups and the next player starts the next round with a Starting Bid.
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Play continues until a single player with dice remains who is then the WINNER!