Liar's Dice

Game Flow Overview
1. Preparation Phase: Create a room or join another player's room (you can also choose to play against AI). Once players are ready, the host or the system starts the game.
2. Dice Rolling Phase: Each player rolls their own dice cup (in this game, shaking their phone). The dice result is only visible to themselves.
3. Reveal Hand: View your hand on the "Reveal Hand" screen. You can confirm your hand or choose to roll again before confirming.
4. Bid Bidding and Challenges: Players can bid, check, predict, or call "Liar" to reveal their cards in turn.
5. Revelation and Settlement: After someone calls "Liar" or makes a prediction, all players reveal their dice. The winner and loser of the round are determined according to the rules, and chips are settled. If the rules include "losing a die," the loser loses one die until someone is eliminated or the winning condition is met.

Bid Bidding Rules
Meaning of Bidding
- The bidding format is "Quantity × Number", for example, "3 fours" means: you believe that the total number of dice with a value of 4 (assuming 1 is counted as a wild card) is at least 3.
- Convention for Number 1: 1 is considered a wild card, meaning 1 can be counted as any number from 2, 3, 4, 5, or 6. Therefore, when calculating the "total number of dice with a certain number," you need to calculate: the number of dice with that number + the number of all 1s.
Legal Bidding
- Opening Bid: When there is no current bid on the table, the current player can bid any legal "quantity × number of points" (e.g., 1×1 to multiple ×6, depending on the room rules).
- Call/Raise: When there is already a current bid, your bid must be "strictly larger":
- Method 1: Larger quantity, any number of points. For example, if the current bid is 3×4, you can bid 4×4, 5×3, etc.
- Method 2: Same quantity, then the number of points must be larger. For example, if the current bid is 3×4, you can bid 3×5, 3×6.
- Bids that do not meet either of the above two conditions are invalid and will be rejected by the system.
Bidding Strategy Overview
- You only know your own dice roll. Based on the current bids, the number of players, and the information already played, you need to estimate the total number of that number on the table to decide whether to raise, check, or reveal.
- You can "boast": bid a higher amount than the actual possible amount, betting that the opponent won't reveal; if the opponent reveals and the actual number is insufficient, you lose.

Player Actions
On your turn, you can generally choose:
| Action | Description |

| Bid | Bid a higher amount ("amount × points") than the current bid, becoming the new current bid. |
| Pass | Do not bid higher this round, passing the turn to the next player (whether this is allowed depends on the current version). |
| Prophecy | Bid a number ("amount × points") that you believe the total number of that number on the table is exactly equal to"; if the actual number revealed is exactly equal to your predicted number, the prediction is successful, and there are additional rewards in this game (such as experience points). | Liar (Showing Hands/Calling a Liar) | Challenges the current bet and requires all players to reveal their dice. The winner is determined by comparing the actual number of dice to the current bet amount.
Liar (Showing Hands) Determination Rules
- When a player chooses Liar, all players reveal all their dice.
- Statistics: Count the "points" of the current bet. Any die with that number or a wild card (1) is counted as 1. The total count is the "actual number of dice."
- Winner/Loser:
- If actual number of dice ≥ current bet amount: The current bettor wins, and the challenger who called Liar loses.
- If actual number of dice < current bet amount: The challenger wins, and the bettor loses.
- The loser loses chips or one die according to the room rules; the winner gains chips for the round or maintains/increases their advantage.