Last Updated: September 19, 2019

# Frenzy Disks - 16 Balls

## Introduction

Frenzy Disks (16 Numbers) is a roulette variation by Red Rake Gaming. Two concentric wheels have 25 numbers and 8 balls each. Like keno, the object is to predict which numbers the balls will land in.

## Rules

1. The game features two concentric roulette wheels. The inner wheel contains all 25 even numbers from 2 to 50. The outer wheel contains all 25 odd numbers from 2 to 50.
2. The player makes a bet, which will be divided into two equal parts, one for each wheel.
3. The player picks eight even and eight odd numbers.
4. The game shall release 16 balls, 8 to the inner wheel and 8 to the outer wheel. Each ball will land in a unique number.
5. The player is paid according to how many chosen numbers match where the balls land. The pay table below shows the pay table.
6. The player may also earn a multiplier according to the lesser number of matches of the two wheels. The multiplier table is also shown below.

The following pay table is for the inner and outer wheels. Wins are based on the bet for that wheel (or half of the total bet).

### Pay Table

Matches Pays
8 1500
7 200
6 30
5 2
4 1.2
3 0.6
2 0
1 0
0 0

The following multiplier table. The multiplier earned is based on the lesser number of matches of the two wheels.

### Multiplier Table

Matches Multiplier
8 10
7 8
6 6
5 4
4 3
3 2
2 1
1 1
0 1

## Example

In the image above, the number of matches is 4 red numbers and 5 blue numbers. The total bet was 2€, or 1€ per wheel. Matching 4 numbers on the red wheel pays 1.2€ and matching 5 on the blue wheel pays 2€. You can tell the number of matches by comparing the chosen numbers (which are highlighted on the field of numbers) and the display of the "latest numbers." The lesser number of matches of the two wheels is 4. The multiplier for 4 matches is 3. Thus, the total win is 4×(1.2 + 2) = 9.6€.

## Analysis

The following table shows the expected win per wheel. The lower right cell shows that the player can expect to win back 57.97% of his bet per wheel, before considering the multiplier.

### Expected Win Per Wheel

Event Pays Combinations Probability Return
8 1500 1 0.000001 0.001387
7 200 136 0.000126 0.025149
6 30 3,808 0.003521 0.105624
5 2 38,080 0.035208 0.070416
4 1.2 166,600 0.154035 0.184842
3 0.6 346,528 0.320392 0.192235
2 0 346,528 0.320392 0.000000
1 0 155,584 0.143849 0.000000
0 0 24,310 0.022476 0.000000
Total   1,081,575 1.000000 0.579652

One cannot simply multiply the expected win by the expected multiplier, because the win and the multiplier are correlated. To get at the overall return, one must consider all possible outcomes of the inner and outer wheels. To begin, the following table shows the probability of all possible number of matches of the inner and outer wheels, rounded to six decimal places. The number of Blue Matches is shown along the column headings.

### Probability of Number of Matches of Both Wheels

Red Matches 8 7 6 5 4 3 2 1 0 Total
8 0 0 0 0 0 0 0 0 0 0.000001
7 0 0 0 0.000004 0.000019 0.00004 0.00004 0.000018 0.000003 0.000126
6 0 0 0.000012 0.000124 0.000542 0.001128 0.001128 0.000506 0.000079 0.003521
5 0 0.000004 0.000124 0.00124 0.005423 0.01128 0.01128 0.005065 0.000791 0.035208
4 0 0.000019 0.000542 0.005423 0.023727 0.049351 0.049351 0.022158 0.003462 0.154035
3 0 0.00004 0.001128 0.01128 0.049351 0.102651 0.102651 0.046088 0.007201 0.320392
2 0 0.00004 0.001128 0.01128 0.049351 0.102651 0.102651 0.046088 0.007201 0.320392
1 0 0.000018 0.000506 0.005065 0.022158 0.046088 0.046088 0.020693 0.003233 0.143849
0 0 0.000003 0.000079 0.000791 0.003462 0.007201 0.007201 0.003233 0.000505 0.022476
Total 0.000001 0.000126 0.003521 0.035208 0.154035 0.320392 0.320392 0.143849 0.022476 1

The next table shows the total win of both wheels according to the number of matches on each. The column headings are the number of blue number matches.

### Total Win of Both Wheels

Red Matches 8 7 6 5 4 3 2 1 0
8 30000 13600 9180 6008 4503.6 3001.2 1500 1500 1500
7 13600 3200 1380 808 603.6 401.2 200 200 200
6 9180 1380 360 128 93.6 61.2 30 30 30
5 6008 808 128 16 9.6 5.2 2 2 2
4 4503.6 603.6 93.6 9.6 7.2 3.6 1.2 1.2 1.2
3 3001.2 401.2 61.2 5.2 3.6 2.4 0.6 0.6 0.6
2 1500 200 30 2 1.2 0.6 0 0 0
1 1500 200 30 2 1.2 0.6 0 0 0
0 1500 200 30 2 1.2 0.6 0 0 0

The next table multiplies the previous two tables to get the overall return according to the number of matches from the two wheels. The lower right cell shows an overall return of the game of 96.07%.

### Total Return of Both Wheels

Red Matches 8 7 6 5 4 3 2 1 0 Total
8 0 0.000001 0.000015 0.000098 0.000321 0.000445 0.000222 0.0001 0.000016 0.001216
7 0.000001 0.000025 0.000305 0.001789 0.005845 0.008082 0.004029 0.001809 0.000283 0.022167
6 0.000015 0.000305 0.002231 0.007933 0.025381 0.034518 0.016921 0.007597 0.001187 0.096088
5 0.000098 0.001789 0.007933 0.009917 0.026032 0.029329 0.01128 0.005065 0.000791 0.092233
4 0.000321 0.005845 0.025381 0.026032 0.085416 0.088833 0.029611 0.013295 0.002077 0.27681
3 0.000445 0.008082 0.034518 0.029329 0.088833 0.123181 0.030795 0.013826 0.00216 0.331169
2 0.000222 0.004029 0.016921 0.01128 0.029611 0.030795 0 0 0 0.092858
1 0.0001 0.001809 0.007597 0.005065 0.013295 0.013826 0 0 0 0.041691
0 0.000016 0.000283 0.001187 0.000791 0.002077 0.00216 0 0 0 0.006514
Total 0.001216 0.022167 0.096088 0.092233 0.27681 0.331169 0.092858 0.041691 0.006514 0.960747