# 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

1. There are six bets available, one for each face on a six-sided die.
2. 15 dice are shaken. A special shaker is used for the game.
3. If the number the player bet on appears on at least six dice, then his bet shall pay 2 to 1.
4. Otherwise, if the number the player bet on appears on three to five dice, then his bet shall pay 1 to 1.
5. 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