Shockwave

Introduction

Shockwave offers a distinct take on video poker. The gameplay is generally standard, referred to as 'regular mode.' However, when a player achieves four of a kind, they trigger 'Shockwave mode.' This mode starts with the subsequent play and continues for ten plays or until another four of a kind appears, whichever comes first. Within Shockwave mode, hitting four of a kind grants a payout of 800 for each coin wagered, based on maximum coin play.

The strategy for playing Shockwave becomes significantly more aggressive after achieving four of a kinds in regular mode and reaches extreme aggression during Shockwave mode. My calculations presume that the average number of plays in Shockwave mode is 9.8836. The value derived from Shockwave mode fluctuates between 18.3 to 18.8, depending on the paytable. Therefore, an optimal strategy in regular mode should incorporate an addition of 18.3 to 18.8 to the payout for a four of a kind. The 'regular mode' tables below illustrate a four of a kind payout ranging from 43.3 to 43.8, even though the actual payout remains at 25. The combined table represents a weighted average of both regular and Shockwave modes, with the exact ratio reliant on the particular paytable; for the 12/8/5 configuration, it is approximately 97.78% regular mode and 2.22% Shockwave mode.

12/8/5

11/8/5

10/8/5

10/7/5

9/6/5

9/6/4

I've received questions regarding my calculations on the distribution between Regular Mode and Shockwave Mode. Here’s the method I used:

1. I recorded the likelihood of achieving a four of a kind in Shockwave mode using the 12/8/5 paytable, noted as 0.0026166. Though this probability may vary slightly across different paytables, I opted to use this consistent figure for simplicity's sake.
2. Keep in mind, Shockwave Mode consists of ten spins, or continues until another four of a kind is achieved, whichever occurs first. The anticipated number of spins in Shockwave Mode is calculated at 9.8830694. This is derived by summing the probabilities from 1 to 10 of i spins, using the formula (1-0.0026166).^(i-1)× 0.0026166, except the probability of 10 spins is (1-0.0026166)¹⁰.
3. The chance of hitting a four of a kind in regular mode stands at 0.0022956 under the 12/8/5 paytable. Therefore, the estimated number of Shockwave spins per regular spin is calculated as 0.0022956 × 9.8830694 = 0.022687259.
4. The probability that a randomly selected spin falls under the regular category is calculated as 1/(1+0.022687259) = 0.977816034. Consequently, the probability for a Shockwave spin is 0.022687259/(1+0.022687259) = 0.022183966.
5. Overall probability of achieving three of a kind under the 12/8/5 paytable is determined using the formula: pr(regular spin) × pr(three of a kind in regular spin) + pr(shockwave spin) × pr(three of a kind in shockwave spin) = 0.977816034 × 0.0708849 + 0.022183966 × 0.0834835 = 0.0711644.

Written by: Michael Shackleford