Fun Dice

Introduction

FunDice is a simple game based on the throw of six ten-sided dice. Each die is numbered from 0 to 9. After the throw, the six dice are lined up randomly to represent a number from 0 to 999,999. A slider is used to set the over/under line and then the player bets whether the next roll will be over or under that number. The game is by FunFair, a software provider for Internet casinos.

Rules

1. First, the player may adjust a slider between an over/under line of 100,000 and 890,000. If the player doesn't touch it, the default setting is 500,000.
2. The player may bet whether the next roll will be over or under the chosen line from rule 1.
3. The win for both the under and over bet are inversely proportional to the probability of winning. To be more specific, the winning odds are the ratio of 0.98 to the probability of winning, rounded to the nearest 1/10.
4. Six pentagonal trapezohedrons (10-sided dice), each numbered 0 to 9, will be rolled and placed in a random order, to simulate a random number drawn from 0 to 999,999.
5. If the number from step 3 is under the line from step 1, then under bets win.
6. If the number from step 3 is equal or over the line from step 1, then over bets win.

Analysis

The following table shows the win and the expected return for variously randomly selected over/under lines. The left two columns show that the return is never far from 98%.

FunDice Analysis

Over/Under Under
Pays
Over
Pays
Under
Return
Over
Return
100000 9.80 1.09 98.00% 98.10%
120000 8.17 1.11 98.04% 97.68%
170000 5.76 1.18 97.92% 97.94%
250000 3.92 1.31 98.00% 98.25%
320000 3.06 1.44 97.92% 97.92%
450000 2.18 1.78 98.10% 97.90%
500000 1.96 1.96 98.00% 98.00%
530000 1.85 2.09 98.05% 98.23%
610000 1.61 2.51 98.21% 97.89%
780000 1.26 4.45 98.28% 97.90%
890000 1.10 8.91 97.90% 98.01%