# Color Match Royals

## Introduction

Color Match Royals is a video poker that adds additional line items to the pay for a flush, straight flush, and royal flush in the same color. It can be played in 3-, 5-, and 10-play mode. For one to five coins bet per hand, it plays like conventional video poker. If the player bets ten coins per hand, then it enables the extra paying hands. Betting max coins also bumps up the pays on some of the other hands, especially the straight flush from 50 to 200.

Here are examples of each additional hand:

 Black flush Black straight flush Red royal flush

Of course, nothing ever comes free. The price you pay for these extra pay is a fee equal to five coins per line bet. In other words, you must wager 10 coins per line bet, but wins are based on a bet of 5 coins only.

## Analysis

The following table shows the probability and contribution to the return for some known pay tables. The return column is the product of the win, probability and 0.5. The reason for dividing by 2 is wins are based on only half the total wager. The overall returns can be found in the lower right corner of each table.

### 9-7 Jacks or Better

Event Pays Combinations Probability Return
Colored royal flush 400 5,983,421,620 0.000300 0.060035
Colored straight flush 60 34,942,566,604 0.001753 0.052589
Colored flush 4 5,566,090,637,932 0.279237 0.558474
Royal flush 800 423,344,460 0.000021 0.008495
Straight flush 200 2,563,185,108 0.000129 0.012859
Four of a kind 25 27,683,651,292 0.001389 0.017360
Full house 9 154,840,105,068 0.007768 0.034956
Flush 7 238,762,710,912 0.011978 0.041923
Straight 4 119,600,509,600 0.006000 0.012000
Three of a kind 3 746,402,640,764 0.037445 0.056168
Two pair 2 1,482,316,048,664 0.074364 0.074364
Jacks or better 1 2,386,104,457,792 0.119705 0.059852
Nothing 0 9,167,517,237,384 0.459911 0.000000
Total   19,933,230,517,200 1.000000 0.989075

### 8/7 Bonus Poker Deluxe

Event Pays Combinations Probability Return
Colored royal flush 400 5,956,767,124 0.000299 0.059767
Colored straight flush 60 34,804,596,288 0.001746 0.052382
Colored flush 4 5,693,964,394,316 0.285652 0.571304
Royal flush 800 419,393,964 0.000021 0.008416
Straight flush 150 2,398,878,152 0.000120 0.009026
Four of a kind 80 27,829,516,924 0.001396 0.055845
Full house 8 128,704,486,284 0.006457 0.025827
Flush 7 242,212,008,544 0.012151 0.042529
Straight 4 118,792,886,696 0.005960 0.011919
Three of a kind 3 764,318,972,604 0.038344 0.057516
Two pair 1 1,219,925,875,256 0.061201 0.030600
Jacks or better 1 2,469,358,699,500 0.123882 0.061941
Nothing 0 9,224,544,041,548 0.462772 0.000000
Total   19,933,230,517,200 1.000000 0.987072

### 7-6 Bonus

Event Pays Combinations Probability Return
Colored royal flush 400 5,978,559,180 0.000300 0.059986
Colored straight flush 60 34,812,941,900 0.001746 0.052394
Colored flush 4 5,600,887,565,944 0.280982 0.561965
Royal flush 800 420,790,260 0.000021 0.008444
Straight flush 200 2,515,014,788 0.000126 0.012617
Four aces + 2-4 80 677,146,800 0.000034 0.001359
Four 2-4 + A-4 40 1,410,964,676 0.000071 0.001416
Four aces + 5-K 80 2,044,656,020 0.000103 0.004103
Four 2-4 40 4,234,072,744 0.000212 0.004248
Four 5-K 25 19,341,301,100 0.000970 0.012129
Full house 7 149,809,080,300 0.007516 0.026304
Flush 6 236,229,862,132 0.011851 0.035553
Straight 4 118,955,557,072 0.005968 0.011935
Three of a kind 3 750,043,817,468 0.037628 0.056442
Two pair 2 1,432,571,713,320 0.071869 0.071869
Jacks or better 1 2,418,112,138,860 0.121311 0.060655
Nothing 0 9,155,185,334,636 0.459293 0.000000
Total   19,933,230,517,200 1.000000 0.981419

### 9-7-5 Double Bonus

Event Pays Combinations Probability Return
Colored royal flush 400 5,968,406,708 0.000299 0.059884
Colored straight flush 60 34,595,131,076 0.001736 0.052067
Colored flush 4 5,670,732,043,856 0.284486 0.568973
Royal flush 800 420,680,524 0.000021 0.008442
Straight flush 200 2,583,032,188 0.000130 0.012958
Four aces 160 3,229,373,444 0.000162 0.012961
Four 2-4 80 5,645,037,420 0.000283 0.011328
Four 5-K 50 19,406,113,452 0.000974 0.024339
Full house 9 121,551,477,564 0.006098 0.027441
Flush 7 238,602,265,528 0.011970 0.041895
Straight 5 131,691,721,568 0.006607 0.016517
Three of a kind 3 776,660,045,876 0.038963 0.058445
Two pair 1 1,166,281,588,692 0.058509 0.029255
Jacks or better 1 2,522,468,813,920 0.126546 0.063273
Nothing 0 9,233,394,785,384 0.463216 0.000000
Total   19,933,230,517,200 1.000000 0.987776

### 9-5 Double Double Bonus

Event Pays Combinations Probability Return
Colored royal flush 400 5,969,163,508 0.000299 0.059892
Colored straight flush 60 35,151,169,064 0.001763 0.052903
Colored flush 4 5,666,244,668,260 0.284261 0.568522
Royal flush 800 419,348,556 0.000021 0.008415
Straight flush 200 2,603,940,680 0.000131 0.013063
Four aces + 2-4 400 904,752,508 0.000045 0.009078
Four 2-4 + A-4 160 1,624,172,264 0.000081 0.006518
Four aces + 5-K 160 2,374,242,420 0.000119 0.009529
Four 2-4 80 4,027,761,496 0.000202 0.008083
Four 5-K 50 19,429,869,404 0.000975 0.024369
Full house 9 121,953,928,668 0.006118 0.027532
Flush 5 232,510,731,244 0.011664 0.029161
Straight 4 120,028,094,032 0.006022 0.012043
Three of a kind 3 781,129,468,284 0.039187 0.058781
Two pair 1 1,173,426,590,468 0.058868 0.029434
Jacks or better 1 2,549,420,257,428 0.127898 0.063949
Nothing 0 9,216,012,358,916 0.462344 0.000000
Total   19,933,230,517,200 1.000000 0.981272

### 9-6 Triple Double Bonus

Event Pays Combinations Probability Return
Red & black royal flush 400 5,931,690,556 0.000298 0.059516
Red & black straight flush 50 31,396,563,176 0.001575 0.039377
Red & black flush 4 5,687,652,506,360 0.285335 0.570670
Royal flush 800 416,105,668 0.000021 0.008350
Straight flush 200 2,540,138,656 0.000127 0.012743
Four aces + 2-4 800 1,152,903,444 0.000058 0.023135
Four 2-4 + A-4 400 2,210,279,808 0.000111 0.022177
Four aces + 5-K 160 1,984,017,420 0.000100 0.007963
Four 2-4 80 2,753,126,772 0.000138 0.005525
Four 5-K 50 19,239,727,188 0.000965 0.024130
Full house 9 116,629,732,824 0.005851 0.026330
Flush 6 237,475,993,876 0.011914 0.035741
Straight 4 125,165,884,360 0.006279 0.012559
Three of a kind 2 787,494,873,352 0.039507 0.039507
Two pair 1 1,180,245,960,124 0.059210 0.029605
Jacks or better 1 2,575,008,794,952 0.129182 0.064591
Nothing 0 9,155,932,218,664 0.459330 0.000000
Total   19,933,230,517,200 1.000000 0.981917

## Strategy

Sorry, you're on your own with that for now. However, notice that in the case of Double Double Bonus, 68.1% of the return comes from the colored wins, with 56.9% in the colored flushes alone. So, the strategy must be significantly different than conventional video poker.

## Acknowledgements

I would like to thank Gary J. Koehler for his confirmation of my analysis.