Shockwave

Introduction

Shockwave is a unique version of video poker. The play is normal most of the time, what I call "regular mode." However, if the player gets a four of a kind, he enters "Shockwave mode." Shockwave mode begins with the next play and lasts for ten plays or until the player gets another four of a kind, whichever happens first. In Shockwave mode a four of a kind pays 800 per coin bet, based on max coins played.

The strategy for Shockwave goes is more aggressive after the four of a kinds in regular mode and extremely agressive in Shockwave mode. My analysis assumed that the average number of games in Shockwave mode is 9.8836. The value of Shockwave mode ranges from 18.3 to 18.8, depending on the pay table. So proper strategy in regular mode should be based on adding 18.3 to 18.8 to the value of a four of a kind. The "regular mode" tables below reflect a four of a kind paying 43.3 to 43.8, although the actual payoff is still 25. The combined table is a weighted average of regular mode and Shockwave mode. The exact mix depends on the pay table but for 12/8/5 is it 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 been asked how I got the mix between Regular Mode and Shockwave Mode. Here is how I did it:

1. I noted the probability of a four of a kind in Shockwave mode in the 12/8/5 pay table, as 0.0026166. While this probability will be slightly different four different pay tables, I assumed this probability for all pay tables, to keep things simple.
2. Remember, Shockwave Mode is ten spins, or until another four of a kind, whichever happens first. The expected number of spins in Shockwave Mode is 9.8830694. This can be found by taking the sum of i from 1 to 10 of the probability of i spins, as (1-0.0026166)^(i-1) × 0.0026166, except the probability of 10 spins is (1-0.0026166)¹⁰.
3. The probability of Four of a Kind in regular mode is 0.0022956, under the 12/8/5 pay table. So, the expected number of Shockwave spins, per regular spin, is 0.0022956 × 9.8830694 = 0.022687259.
4. The probability that any given spin is a regular spin is 1/(1+0.022687259) = 0.977816034. The probability it is a Shockwave spin is 0.022687259/(1+0.022687259) = 0.022183966.
5. The overall probability of a three of a kind under the 12/8/5 pay table, for example, is 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