# Double Big Wheel Poker

## Introduction

Double Big Wheel Poker is a simple video poker game with a random multiplier. It is played as an optional feature to 3-play, 5-play, and 10-play video poker. If the player pays 10 coins per line, wins will be based on a 5-coin bet, but be eligible for a random multiplier.

## Rules

1. Double Big Wheel Poker is an optional feature based on 3-play, 5-play, and 10-play video poker.
2. If the player bets 1 to 5 coins per play, then the game plays like conventional multi-play video poker.
3. If the player bets 10 coins per play, then the player will be eligible for the Double Big Wheel feature.
4. If the Double Big Wheel is enabled, then randomly, with a 1 in 5.049 chance per deal, the feature will be activated.
5. If the feature is activated, then two concentric wheels will spin.
6. The outer wheel has multipliers from 1x to 4x.
7. The inner wheel has multiplier from 2x to 4x.
8. With the feature activated, the player will get a multiplier equal to the product of the inner wheel and outer wheel. For example, if the outer wheel is 3x and the inner wheel is 4x, then the player will get a 12x multiplier.
9. The average feature multiplier is 6.05.
10. With the feature enabled, wins are based on a five-coin bet.

## Analysis

The outer wheel has four slices each of 1x, 2x, 3x, and 4x multipliers. If each slice were equally likely, then the average outer wheel multiplier would be 2.5.

The inner wheel has five 2x, five 3x, and 2 4x multipliers. If each slice were equally likely, then the average inner wheel multiplier would be 33/12 = 2.75.

• Taking the product of the average multiplier yields 2.5 × 2.75 = 6.875. However, the game help files indicate an average multiplier of 6.05. This would indicate the wheel slices are not equally likely and the wheels are more likely to stop on the slices with lower multipliers.

That said, the average overall multiplier, is: pr(multiplier)×6.05 + pr(no multiplier)× 1 = (1/5.049)×6.05 + (4.049/5.049)×1 = 2.00019806.

Given that the player must pay a fee equal to his five-coin bet amount per line, the expected value with the feature is almost the same as without the feature. To be more specific, if the return without the feature is r, then the return with the feature is r×1.0001.

## Example

In the game above, I was dealt a pair of aces and a multiplier of 12x. I held the aces.

None of the hands improved. With three wins of 5 for the high pair and a multiplier of 12x, my total win was 5×3×12 = 180 credits.

## Return Table

The following table shows the return, with and without the Double Big Wheel Feature, for various popular games and pay tables.

### Reversible Royal Game Summary

Game Pay Table Return without Feature Return with Feature
Bonus Deuces Wild 10-4-4-3 99.860% 99.870%
Bonus Deuces Wild 9-4-4-3 99.450% 99.460%
Bonus Deuces Wild 8-4-4-3 99.146% 99.156%
Bonus Deuces Wild 13-4-3-3 98.803% 98.812%
Bonus Deuces Wild 10-4-3-3 97.364% 97.374%
Bonus Deuces Wild 12-4-3-2 96.218% 96.228%
Bonus Deuces Wild 10-4-3-2 95.337% 95.346%
Bonus Poker 8-5 99.166% 99.176%
Bonus Poker 7-5 98.015% 98.024%
Bonus Poker 6-5 96.869% 96.878%
Bonus Poker 10-8-5-3-1 94.183% 94.192%
Bonus Poker Deluxe 9-6 99.642% 99.652%
Bonus Poker Deluxe 9-5 98.550% 98.559%
Bonus Poker Deluxe 8-6 98.493% 98.503%
Bonus Poker Deluxe 8-5 97.401% 97.411%
Bonus Poker Deluxe 7-5 96.253% 96.262%
Bonus Poker Deluxe 6-5 95.361% 95.371%
Deuces Wild 25-15-9-5-3-2 100.762% 100.772%
Deuces Wild 25-15-11-4-4-3 99.957% 99.967%
Deuces Wild 25-16-10-4-4-3 99.728% 99.738%
Deuces Wild 25-15-10-4-4-3 99.418% 99.428%
Deuces Wild 20-12-9-5-3-2 98.938% 98.948%
Deuces Wild 25-15-9-4-4-3 98.913% 98.923%
Deuces Wild 20-12-10-4-4-3 97.579% 97.589%
Deuces Wild 20-12-9-4-4-3 97.055% 97.065%
Deuces Wild 25-16-13-4-3-2 96.765% 96.775%
Deuces Wild 20-10-8-4-4-3 95.964% 95.973%
Deuces Wild 25-15-10-4-3-2 94.818% 94.828%
Double Bonus 10-7-5 100.173% 100.182%
Double Bonus 9-7-5 99.107% 99.116%
Double Bonus 10-6-5 98.885% 98.894%
Double Bonus 10-7-4 98.814% 98.823%
Double Bonus 9-6-5 97.806% 97.816%
Double Bonus 9-7-4 97.741% 97.751%
Double Bonus 10-6-4 97.461% 97.471%
Double Bonus 9-6-4 96.375% 96.385%
Double Bonus 8-6-5 96.228% 96.237%
Double Bonus 9-5-4 95.274% 95.283%
Double Bonus 8-5-4 94.190% 94.199%
Double Double Bonus 10-6 100.067% 100.077%
Double Double Bonus 9-6 98.981% 98.991%
Double Double Bonus 8-6 97.895% 97.905%
Double Double Bonus 8-5 96.786% 96.796%
Double Double Bonus 7-5 95.712% 95.721%
Jacks or Better 9-6 99.544% 99.554%
Jacks or Better 9-5 98.450% 98.460%
Jacks or Better 8-6 98.393% 98.402%
Jacks or Better 8-5 97.298% 97.308%
Jacks or Better 7-5 96.147% 96.157%
Jacks or Better 6-5 94.996% 95.006%
Joker Poker (kings or better) 800-20-7 100.646% 100.656%
Joker Poker (kings or better) 940-18-7 99.293% 99.303%
Joker Poker (kings or better) 800-18-7 98.937% 98.947%
Joker Poker (kings or better) 940-17-7 98.443% 98.452%
Joker Poker (kings or better) 800-17-7 98.085% 98.095%
Joker Poker (kings or better) 940-15-7 96.744% 96.753%
Joker Poker (kings or better) 800-15-7 96.385% 96.394%
Joker Poker (kings or better) 800-20-5 95.457% 95.466%
Super Aces Bonus 8-5 99.939% 99.949%
Super Aces Bonus 7-5 98.852% 98.861%
Super Aces Bonus 6-5 97.780% 97.789%
Super Double Bonus 9-5 99.695% 99.704%
Super Double Bonus 8-5 98.686% 98.696%
Super Double Bonus 7-5 97.771% 97.780%
Super Double Bonus 6-5 96.871% 96.881%
Triple Double Bonus 9-7 99.578% 99.588%
Triple Double Bonus 9-6 98.154% 98.164%
Triple Double Bonus 8-6 97.109% 97.118%
Triple Double Bonus 9-5 97.020% 97.030%
Triple Double Bonus 8-5 95.969% 95.978%
Triple Double Bonus 7-5 94.918% 94.927%
Triple Double Bonus 6-5 93.867% 93.877%