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Red Dragon
Introduction
I first heard of Red Dragon in October 2019. A friend of mine had an old felt from the game in his collection of antique gambling equipment. I have no idea of its background and can't find any other information about it. The game itself is a simple game of chance utilizing 15 dice.
Rules
- There are six bets available, one for each face on a six-sided die.
- 15 dice are shaken. A special shaker is used for the game.
- If the number the player bet on appears on at least six dice, then his bet shall pay 2 to 1.
- Otherwise, if the number the player bet on appears on three to five dice, then his bet shall pay 1 to 1.
- Otherwise, the bet loses.
The following table shows the Player's Monster pay table. Wins are on a "to one" basis.
Player's Monster Pay Table
| Player Hand | Pays |
|---|---|
| Five aces | 1000 |
| Five of a kind | 200 |
| Royal flush | 100 |
| Straight flush | 40 |
| Four of a kind | 7 |
| Full house | 3 |
| Flush | 2 |
| Straight | 1 |
Analysis
The table below shows the probability of achieving 0 to 15 of a given die face.
The image below is of the shaker used in Red Dragon.
Red Dragon Permutations
| Number | Permutations | Probability |
|---|---|---|
| 15 | 1 | 0.0000000000021 |
| 14 | 75 | 0.0000000001595 |
| 13 | 2,625 | 0.0000000055829 |
| 12 | 56,875 | 0.0000001209630 |
| 11 | 853,125 | 0.0000018144454 |
| 10 | 9,384,375 | 0.0000199588998 |
| 9 | 78,203,125 | 0.0001663241651 |
| 8 | 502,734,375 | 0.0010692267756 |
| 7 | 2,513,671,875 | 0.0053461338781 |
| 6 | 9,775,390,625 | 0.0207905206369 |
| 5 | 29,326,171,875 | 0.0623715619108 |
| 4 | 66,650,390,625 | 0.1417535497972 |
| 3 | 111,083,984,375 | 0.2362559163287 |
| 2 | 128,173,828,125 | 0.2726029803793 |
| 1 | 91,552,734,375 | 0.1947164145566 |
| 0 | 30,517,578,125 | 0.0649054715189 |
| Total | 470,184,984,576 | 1.0000000000000 |
The next return table summarizes these combinations to determine the probability and contribution to the return of each event. The lower right cell shows a house edge of 3.71%.
Red Dragon Return Table
| Number | Pays | Permutations | Probability | Return |
|---|---|---|---|---|
| 6 to 15 | 2 | 12,880,297,076 | 0.027394 | 0.054788 |
| 3 to 5 | 1 | 207,060,546,875 | 0.440381 | 0.440381 |
| 0 to 2 | -1 | 250,244,140,625 | 0.532225 | -0.532225 |
| Total | 470,184,984,576 | 1.000000 | -0.037056 |
External Links
Discussion about Red Dragon in my forum at Wizard of Vegas.