Last Updated: May 3, 2019

# 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

### 12/8/5 Shockwave — Normal Mode

Hand Payoff Combinations Probability Return
Royal flush 800 431106600 0.000022 0.017302
Straight Flush 100 2520154068 0.000126 0.012643
Four of a Kind 25 45758088456 0.002296 0.057389
Full House 12 222750801144 0.011175 0.134098
Flush 8 336240678132 0.016868 0.134947
Straight 5 290724757764 0.014585 0.072925
Three of a kind 3 1412965088916 0.070885 0.212655
Two pair 1 2451947454252 0.123008 0.123008
Pair 1 3734571886848 0.187354 0.187354
Nonpaying hand 0 11435320501020 0.573681 0
Total 19933230517200 1 0.952321

### 12/8/5 Shockwave — Shockwave Mode

Hand Payoff Combinations Probability Return
Royal flush 800 399826968 0.00002 0.016047
Straight Flush 100 2154197724 0.000108 0.010807
Four of a Kind 800 52157949768 0.002617 2.093306
Full House 12 135947069496 0.00682 0.081841
Flush 8 198921205428 0.009979 0.079835
Straight 5 201570677196 0.010112 0.050561
Three of a kind 3 1664096730120 0.083484 0.250451
Two pair 1 1922012037000 0.096423 0.096423
Pair 1 4399064065980 0.22069 0.22069
Nonpaying hand 0 11356906757520 0.569747 0
Total 19933230517200 1 2.899961

### 12/8/5 Shockwave — Combined Modes

Hand Payoff Probability Return
Royal flush 800 0.000022 0.017274
Straight Flush 100 0.000126 0.012602
Four of a kind - Shockwave mode 800 0.000058 0.046438
Four of a kind - Regular mode 25 0.002245 0.056116
Full House 12 0.011078 0.132939
Flush 8 0.016716 0.133724
Straight 5 0.014486 0.072429
Three of a kind 3 0.071164 0.213493
Two pair 1 0.122418 0.122418
Pair 1 0.188094 0.188094
Nonpaying hand 0 0.573594 0
Total 1 0.995527

## 11/8/5

### 11/8/5 Shockwave — Normal Mode

Hand Payoff Combinations Probability Return
Royal flush 800 433356876 0.000022 0.017392
Straight Flush 100 2520008556 0.000126 0.012642
Four of a Kind 25 45749736996 0.002295 0.057379
Full House 11 222721149204 0.011173 0.122907
Flush 8 336318008988 0.016872 0.134978
Straight 5 290746358040 0.014586 0.07293
Three of a kind 3 1412648013624 0.070869 0.212607
Two pair 1 2451547424736 0.122988 0.122988
Pair 1 3734106376932 0.187331 0.187331
Nonpaying hand 0 11436440083248 0.573737 0
Total 19933230517200 1 0.941154

### 11/8/5 Shockwave — Shockwave Mode

Hand Payoff Combinations Probability Return
Royal flush 800 399946920 0.00002 0.016051
Straight Flush 100 2158532076 0.000108 0.010829
Four of a Kind 800 52155877512 0.002617 2.093223
Full House 11 135936627192 0.00682 0.075016
Flush 8 199118575404 0.009989 0.079914
Straight 5 201684259068 0.010118 0.05059
Three of a kind 3 1663992320628 0.083478 0.250435
Two pair 1 1921835577420 0.096414 0.096414
Pair 1 4398655759992 0.220669 0.220669
Nonpaying hand 0 11357293040988 0.569767 0
Total 19933230517200 1 2.893141

### 11/8/5 Shockwave — Combined Modes

Hand Payoff Probability Return
Royal flush 800 0.000022 0.017363
Straight Flush 100 0.000126 0.012602
Four of a kind - Shockwave mode 800 0.000058 0.046428
Four of a kind - Regular mode 25 0.002244 0.056106
Full House 11 0.011077 0.121845
Flush 8 0.01672 0.133757
Straight 5 0.014487 0.072435
Three of a kind 3 0.071149 0.213446
Two pair 1 0.122399 0.122399
Pair 1 0.18807 0.18807
Nonpaying hand 0 0.573649 0
Total 1 0.984449

## 10/8/5

### 10/8/5 Shockwave — Normal Mode

Hand Payoff Combinations Probability Return
Royal flush 800 435378048 0.000022 0.017473
Straight Flush 100 2520708252 0.000126 0.012646
Four of a Kind 25 45732139848 0.002294 0.057357
Full House 10 222633177912 0.011169 0.111689
Flush 8 336425203860 0.016878 0.135021
Straight 5 291202148580 0.014609 0.073044
Three of a kind 3 1411815366612 0.070827 0.212482
Two pair 1 2450210895468 0.122921 0.122921
Pair 1 3734837079372 0.187367 0.187367
Nonpaying hand 0 11437418419248 0.573786 0
Total 19933230517200 1 0.930001

### 10/8/5 Shockwave — Shockwave Mode

Hand Payoff Combinations Probability Return
Royal flush 800 400298316 0.00002 0.016066
Straight Flush 100 2162231280 0.000108 0.010847
Four of a Kind 800 52153675224 0.002616 2.093135
Full House 10 135927023400 0.006819 0.068191
Flush 8 199313496984 0.009999 0.079992
Straight 5 201720386292 0.01012 0.050599
Three of a kind 3 1663898473644 0.083474 0.250421
Two pair 1 1921699387476 0.096407 0.096407
Pair 1 4398545461896 0.220664 0.220664
Nonpaying hand 0 11357410082688 0.569773 0
Total 19933230517200 1 2.886322

### 10/8/5 Shockwave — Combined Modes

Hand Payoff Probability Return
Royal flush 800 0.000022 0.017442
Straight Flush 100 0.000126 0.012606
Four of a kind - Shockwave mode 800 0.000058 0.046408
Four of a kind - Regular mode 25 0.002243 0.056085
Full House 10 0.011073 0.110725
Flush 8 0.016725 0.133801
Straight 5 0.014509 0.072547
Three of a kind 3 0.071108 0.213323
Two pair 1 0.122333 0.122333
Pair 1 0.188106 0.188106
Nonpaying hand 0 0.573697 0
Total 1 0.973375

## 10/7/5

### 10/7/5 Shockwave — Normal Mode

Hand Payoff Combinations Probability Return
Royal flush 800 434842296 0.000022 0.017452
Straight Flush 100 2531533080 0.000127 0.0127
Four of a Kind 25 45955348032 0.002305 0.057637
Full House 10 223709023728 0.011223 0.112229
Flush 7 307603932804 0.015432 0.108022
Straight 5 300759945072 0.015088 0.075442
Three of a kind 3 1421992834248 0.071338 0.214013
Two pair 1 2466011558232 0.123714 0.123714
Pair 1 3831327899712 0.192208 0.192208
Nonpaying hand 0 11332903599996 0.568543 0
Total 19933230517200 1 0.913417

### 10/7/5 Shockwave — Shockwave Mode

Hand Payoff Combinations Probability Return
Royal flush 800 403595316 0.00002 0.016198
Straight Flush 100 2008338456 0.000101 0.010075
Four of a Kind 800 52212950208 0.002619 2.095514
Full House 10 136207087056 0.006833 0.068332
Flush 7 191300200188 0.009597 0.067179
Straight 5 201069037476 0.010087 0.050436
Three of a kind 3 1666587926520 0.083609 0.250826
Two pair 1 1925855597160 0.096615 0.096615
Pair 1 4412364907680 0.221357 0.221357
Nonpaying hand 0 11345220877140 0.569161 0
Total 19933230517200 1 2.876532

### 10/7/5 Shockwave — Combined Modes

Hand Payoff Probability Return
Royal flush 800 0.000022 0.017424
Straight Flush 100 0.000126 0.012642
Four of a kind - Shockwave mode 800 0.000058 0.046683
Four of a kind - Regular mode 25 0.002254 0.056353
Full House 10 0.011125 0.111251
Flush 7 0.015302 0.107112
Straight 5 0.014977 0.074885
Three of a kind 3 0.071611 0.214833
Two pair 1 0.12311 0.12311
Pair 1 0.192857 0.192857
Nonpaying hand 0 0.568557 0
Total 1 0.95715

## 9/6/5

### 9/6/5 Shockwave — Normal Mode

Hand Payoff Combinations Probability Return
Royal flush 800 493826880 0.000025 0.019819
Straight Flush 100 2535528228 0.000127 0.01272
Four of a Kind 25 46370798724 0.002326 0.058158
Full House 9 226126238436 0.011344 0.102098
Flush 6 233529020352 0.011716 0.070293
Straight 5 311039048652 0.015604 0.07802
Three of a kind 3 1443978065532 0.072441 0.217322
Two pair 1 2504547506412 0.125647 0.125647
Pair 1 4064521893840 0.203907 0.203907
Nonpaying hand 0 11100088590144 0.556864 0
Total 19933230517200 1 0.887984

### 9/6/5 Shockwave — Shockwave Mode

Hand Payoff Combinations Probability Return
Royal flush 800 422015244 0.000021 0.016937
Straight Flush 100 1880772528 0.000094 0.009435
Four of a Kind 800 52270556448 0.002622 2.097826
Full House 9 136438757136 0.006845 0.061603
Flush 6 181460029068 0.009103 0.05462
Straight 5 200335673364 0.01005 0.050252
Three of a kind 3 1669180132488 0.083739 0.251216
Two pair 1 1929830203224 0.096815 0.096815
Pair 1 4418209712268 0.22165 0.22165
Nonpaying hand 0 11343202665432 0.56906 0
19933230517200 1 2.860354

### 9/6/5 Shockwave — Combined Modes

Hand Payoff Probability Return
Royal flush 800 0.000025 0.019754
Straight Flush 100 0.000126 0.012646
Four of a kind - Shockwave mode 800 0.000059 0.047147
Four of a kind - Regular mode 25 0.002274 0.056851
Full House 9 0.011243 0.101188
Flush 6 0.011657 0.069941
Straight 5 0.015479 0.077396
Three of a kind 3 0.072695 0.218084
Two pair 1 0.124999 0.124999
Pair 1 0.204306 0.204306
Nonpaying hand 0 0.557138 0
Total 1 0.932312

## 9/6/4

### 9/6/4 Shockwave — Normal Mode

Hand Payoff Combinations Probability Return
Royal flush 800 491193384 0.000025 0.019714
Straight Flush 100 2588354208 0.00013 0.012985
Four of a Kind 25 46678620588 0.002342 0.058544
Full House 9 227475141372 0.011412 0.102707
Flush 6 243484958388 0.012215 0.07329
Straight 4 255258457848 0.012806 0.051223
Three of a kind 3 1461656381892 0.073328 0.219983
Two pair 1 2537266212468 0.127288 0.127288
Pair 1 4131401175684 0.207262 0.207262
Nonpaying hand 0 11026930021368 0.553193 0
Total 19933230517200 1 0.872995

### 9/6/4 Shockwave — Shockwave Mode

Hand Payoff Combinations Probability Return
Royal flush 800 424954380 0.000021 0.017055
Straight Flush 100 1937261112 0.000097 0.009719
Four of a Kind 800 52279265496 0.002623 2.098175
Full House 9 136502618328 0.006848 0.061632
Flush 6 183075854688 0.009184 0.055107
Straight 4 192466587708 0.009656 0.038622
Three of a kind 3 1670354754888 0.083797 0.251392
Two pair 1 1932779273256 0.096963 0.096963
Pair 1 4420872962676 0.221784 0.221784
Nonpaying hand 0 11342536984668 0.569027 0
19933230517200 1 2.850449

### 9/6/4 Shockwave — Combined Modes

Hand Payoff Probability Return
Royal flush 800 0.000025 0.019653
Straight Flush 100 0.000129 0.012911
Four of a kind - Shockwave mode 800 0.000059 0.047461
Four of a kind - Regular mode 25 0.002289 0.057219
Full House 9 0.011309 0.101778
Flush 6 0.012146 0.072879
Straight 4 0.012734 0.050938
Three of a kind 3 0.073564 0.220693
Two pair 1 0.126602 0.126602
Pair 1 0.20759 0.20759
Nonpaying hand 0 0.553551 0
Total 1 0.917725

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.

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