Moving Multipliers

Introduction

Moving Multipliers is a video poker variant that can be added to conventional multi-play machines. With an extra three coins bet per line, the player invokes the Moving Multipliers feature. The feature randomly gives the player random multipliers from 2x to 12x.

For those already familiar with Haywire Poker, Moving Multipliers is the same except the multipliers stay the same as they move, as opposed to being redrawn each time.

Rules

Moving Multipliers is a feature added to conventional 3-, 5-, and 10-play multi-play video poker machines. It is assumed the reader is already familiar with how multi-play poker works.
If the player bets a maximum eight coins per hand, then he activates the feature. The player will still be betting five coins per line. The extra three coins are a fee for the feature.
With the feature on, the game will award the player a multiplier to the bottom hand with probability 11.4942529%.
The multiplier can be 2, 3, 4, 5, 6, 8, 10, or 12, each with equal probability.
A multiplier on the bottom hand will move to another hand on the screen with the next hand to be played.
The multiplier will remain the same as it travels from hand to hand.
After a multiplier has covered every hand on the screen, it will fall off.
During the process of this moving multiplier, new multipliers can appear in the bottom hand. Thus, multiple multipliers can appear on the screen at the same time. When this happens, they will be separately drawn. In other words, multiple hands can have different multipliers on the same play.

Example

In the image above, the bottom hand was awarded a multiplier of 10x. Yes, I know that holding a high pair beats three to a royal.

In the next hand, the multiplier moves to the middle hand.

In the next hand, the multiplier moves to the top hand.

Analysis

The average multiplier, when there is one, is 6.25. The exact probability of getting a multiplier, other than 1, is 114,942,529/1,000,000,000. The rule screens show 11.49% but to be more precise it is 11.494252952381%. Considering the chance of a multiplier, the overall average multiplier, including those 88.51% of hands when there isn't one, is 0.11494253 ×6.25 + (1-0.11494253)×1 = 1.603225. Considering the win is based on only 5/8 of the amount bet, the overall increase in return, compared to conventional video poker is (5/8)×1.603225 = 1.002155173. Thus, you can get the return in Moving Multipliers by multiplying the conventional return by 1.002155173. As a quick estimate, you could also simply add 0.21%.

The following table shows the return for both the base game as well as with the Moving Multipliers feature for games and pay tables for which Moving Multipliers is available.