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Last Updated: July 15, 2013

Match Card Video Poker

Introduction



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Introduction

I noticed Triple Play Draw Poker with Match Card at the Peppermill casino in Reno in June 2013. The game plays like triple-play video poker, but with a twist. The twist is after the draw, the game will choose three cards, known as the Match Cards, from a separate deck, not including any cards the player discarded. If the Match Cards match any cards in the player's hand after the draw, then he will win multipliers. The cost is that the player must double his bet, and wins are based on half the total bet only.

Rules

  1. The player makes a 30-credit bet. 15 credits are for three hands of five credits each, based on standard Triple Play video poker. The other 15 credits are to enable the Match Card feature.
  2. The player will be given a single hand on the deal.
  3. The player will choose which cards to hold and draw new ones to replace the discards.
  4. The game will replace the discards. Each hand is dealt replacement cards from a separate deck containing the remaining 47 cards.
  5. The game will also choose three cards from another separate deck, not including any discards, as the Match Cards. The game will display the cards from top to bottom.
  6. The player will earn multipliers according to the number of cards in his hand that match the Match Cards, according to the table below.
  7. The player will be paid according to the poker value of his hand and any multipliers.

Multiplier Table

Match Multiplier
Top 3
Middle 4
Bottom 5
Two or more 11

Example

In the example on the right, I was dealt a pair of deuces on the deal, which I held. On the draw, the top hand was garbage, the middle hand improved to a full house, and the bottom one improved to a three of a kind. You can't see the middle card of the bottom hand, so take it on faith that it was the two of spades.

The three Match Cards are shown on the right of the screen. The one in the bottom position was the two of spades, which matched a card in both the middle and bottom hands. According to the multiplier table above, matching the bottom Match Card earns a 5x multiplier. My full house in the middle hand would normally pay 45 credits, but with the multiplier it paid 5 × 45 = 225. My three of a kind in the bottom hand would normally pay 15 credits, but with the multiplier it paid 15 × 5 = 75. So, my total win was 225 + 75 = 300 credits.

Odds for 9-5 Jacks or Better

The following table shows the number of combinations of each hand on the draw by the number of discards. The number of discards is pertinent, because the more cards that are discarded, the greater the odds for a multiplier.

As usual for my video poker analysis, I always assume optimal player strategy.

Combinations in 9-5 Jacks or BetterExpand

Hand Discards
0 1 2 3 4 5 Total
Royal flush 30,678,780 152,741,160 201,185,820 95,192,196 17,492,916 1,426,800 498,717,672
Straight flush 276,109,020 1,032,634,680 748,976,580 86,848,476 26,193,708 7,725,060 2,178,487,524
Four of a kind - 75 - 4,785,889,680 17,921,629,440 23,332,032,372 46,039,551,567
Full house 28,715,338,080 80,647,332,480 25,713,642,240 88,335,423,396 5,247,497,088 895,903,200 229,555,136,484
Flush 37,980,329,640 133,224,886,740 25,704,957,960 13,861,121,208 6,641,041,776 1,258,305,540 218,670,642,864
Straight 77,678,670,960 91,789,604,280 15,047,984,160 26,682,308,400 10,049,277,504 2,411,904,300 223,659,749,604
Three of a kind - - 383,450,977,800 1,013,480,819,340 74,740,392,552 13,287,543,600 1,484,959,733,292
Two pair - 866,958,824,160 17,783,872,920 1,501,392,935,196 161,688,504,024 30,286,083,600 2,578,110,219,900
Jacks or better - 92,790,254,700 111,682,905,840 3,138,943,393,080 826,809,283,152 101,940,624,000 4,272,166,460,772
Nothing - 965,192,930,460 539,497,102,320 6,711,113,411,904 2,163,728,054,268 496,780,854,900 10,876,312,353,852
Total 144,681,126,480 2,231,789,208,735 1,119,831,605,640 12,498,777,342,876 3,266,869,366,428 670,202,403,372 19,932,151,053,531

The following table shows the probability of each hand by number of discards, to six decimal places.

Probabilities in 9-5 Jacks or Better

Hand Discards
0 1 2 3 4 5 Total
Royal flush 0.000002 0.000008 0.000010 0.000005 0.000001 0.000000 0.000025
Straight flush 0.000014 0.000052 0.000038 0.000004 0.000001 0.000000 0.000109
Four of a kind 0.000000 0.000000 0.000000 0.000240 0.000899 0.001171 0.002310
Full house 0.001441 0.004046 0.001290 0.004432 0.000263 0.000045 0.011517
Flush 0.001905 0.006684 0.001290 0.000695 0.000333 0.000063 0.010971
Straight 0.003897 0.004605 0.000755 0.001339 0.000504 0.000121 0.011221
Three of a kind 0.000000 0.000000 0.019238 0.050847 0.003750 0.000667 0.074501
Two pair 0.000000 0.043495 0.000892 0.075325 0.008112 0.001519 0.129344
Jacks or better 0.000000 0.004655 0.005603 0.157481 0.041481 0.005114 0.214335
Nothing 0.000000 0.048424 0.027067 0.336698 0.108555 0.024924 0.545667
Total 0.007259 0.111969 0.056182 0.627066 0.163899 0.033624 1.000000

The next table shows the average multiplier according to number of discards. This illustrates the advantage of discarding more cards.

Average Multiplier Table

Discard Average
Multiplier
0 1.950905
1 1.971188
2 1.992347
3 2.014438
4 2.037523
5 2.061671

The next table shows the contribution to the return for each hand and number of discards. Each cell is the product of the probability, base win, average multiplier, and 0.5. The reason for dividing by 2 is the win is based on half the bet only. The lower right cell shows an overall return of 98.592%. This return is 0.004% lower than the 98.596% return published by IGT.

Returns in 9-5 Jacks or Better

Hand Pays Discards
0 1 2 3 4 5 Total
Royal flush 800 0.001201 0.006042 0.008044 0.003848 0.000715 0.000059 0.019910
Straight flush 50 0.000676 0.002553 0.001872 0.000219 0.000067 0.000020 0.005407
Four of a kind 25 0.000000 0.000000 0.000000 0.006046 0.022900 0.030167 0.059113
Full house 9 0.012648 0.035890 0.011566 0.040174 0.002414 0.000417 0.103109
Flush 5 0.009294 0.032938 0.006423 0.003502 0.001697 0.000325 0.054180
Straight 4 0.015206 0.018155 0.003008 0.005393 0.002055 0.000499 0.044316
Three of a kind 3 0.000000 0.000000 0.057493 0.153641 0.011460 0.002062 0.224655
Two pair 2 0.000000 0.085738 0.001778 0.151738 0.016528 0.003133 0.258914
Jacks or better 1 0.000000 0.004588 0.005582 0.158618 0.042259 0.005272 0.216320
Nothing 0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
Total 0.039024 0.185905 0.095765 0.523180 0.100096 0.041953 0.985923

The following table shows the probability of discarding 0 to 5 cards in both conventional video poker and Match Card for 9-5 Jacks or Better.

Number of Discards

Discard Standard
Video
Poker
Match
Card
5 0.032459 0.033624
4 0.157101 0.163899
3 0.634588 0.627066
2 0.055910 0.056182
1 0.112684 0.111969
0 0.007258 0.007259
Total 1.000000 1.000000

On average, for 9-5 Jacks or Better the player will discard 2.918968 cards, and in Match Card the player will discard 2.929251 cards on average. In other words, in Match Card the player will discard 0.010283 more cards per hand.

Playing standard 9-5 Jacks or Better in this game, including discarding the singleton with a dealt four of a kind, will result in a return of 0.985946. Compared to optimal Match Card strategy, the cost of errors is 0.000023.

Other Pay Tables

The following table shows the games, pay tables, and returns this Match Card is available in. The table was kindly provided by IGT. As noted before, the IGT return for 9-5 Jacks or Better is 0.000037 higher than my figure. I do not know the cause for this disparity, but am not going to lose any sleep over it.

All Games and Pay Tables

Game Pay Table Return
JACKS OR BETTER 9/5 98.60%
JACKS OR BETTER 8/5 97.45%
JACKS OR BETTER 7/5 96.31%
BONUS POKER 8/5 (4 2s,3s,4s = 45; 4 5s-Ks = 20) 98.76%
BONUS POKER 7/5 (4 2s,3s,4s = 45; 4 5s-Ks = 20) 97.62%
BONUS POKER 6/5 (4 2s,3s,4s = 40; 4 5s-Ks = 20) 96.22%
BONUS POKER DLX 9/5 98.67%
BONUS POKER DLX 8/5 97.53%
BONUS POKER DLX 7/5 96.47%
DEUCES WILD 25/15/9/4/4/3 98.92%
DEUCES WILD 25/15/10/4/3/3 96.89%
DEUCES WILD 25/15/8/4/3/3 95.95%
DEUCES BONUS 12/4/3/3 98.40%
DEUCES BONUS 10/4/3/3 97.51%
DEUCES BONUS 12/4/3/2 96.40%
DOUBLE BONUS 9/7/5 99.12%
DOUBLE BONUS 9/6/5 97.90%
DOUBLE BONUS 9/5/5 96.83%
DOUBLE DBL BONUS 10/5/4 99.14%
DOUBLE DBL BONUS 9/5/4 98.06%
DOUBLE DBL BONUS 8/5/4 96.98%
TRIPLE DBL BONUS 9/5/5 98.53%
TRIPLE DBL BONUS 8/5/5 97.49%
TRIPLE DBL BONUS 7/6/4 96.13%

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Written by: Michael Shackleford

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