# Xtra Card

## Introduction

Xtra Card is a video poker variant by Aristocrat. It can be played as an added feature to single-play and triple-play video poker. If the player bets ten credits per play, then he will have a chance at getting extra hands and a multiplier. The game can be found on multi-game machines that say "Winner's World Multi-Game" and "Storming Jackpots" above the main screen.

## Rules

1. The game is based on single-play for three-play video poker, which I assume the reader is familiar with.
2. If the player bets 1 to 5 credits per play, then the game will play as conventional video poker.
3. If the player bets ten credits per play, then he will have a chance at invoking the feature. With a ten-credit bet per play, wins will be based on five credits per play, with the additional wager being a non-refundable fee for a chance at the feature.
4. If the player bets 10 credits per play, then each play will have a chance of triggering the feature, according to the number of cards held. These probabilities vary slightly from game to game. Following is an example for 8-6 Bonus Poker Deluxe:
• 0 cards held = 30.24%
• 1 cards held = 25.03%
• 2 cards held = 19.43%
• 3 cards held = 13.42%
• 4 cards held = 6.95%
• 5 cards held = 0.00%
5. If the feature is triggered, that play will get one or two extra hands. The chances of one extra hand is 25% and two is 75%.
6. If the feature is triggered, in addition to the extra hands, the original and extra hands shall have a 40% chance at a multiplier.
7. The possible multipliers are 2x, 3x, 4x, 5x, 6x, 8x or 10x. The average multiplier is 4.8.

## Example

In the image above, the player bet on one play. After holding a pair of queens, the game awarded the player two extra hands and a multiplier of 5x. One of the three hands improved to a three of a kind and the other two remained as a high pair. The total win was 5×(5 + 5 + 15) = 75.

## Analysis

If the feature is activated, the probability of one extra hand is 25% and two is 75%. That makes the average total hands, including the original hand 1 + (0.25*2 + 0.75*3) = 2.75.

With a 40% chance at an average multiplier of 4.8, the overall average multiplier (including 1x for no multiplier) is 0.6*1 + 0.4*4.8 = 2.52.

This makes the average value of the feature, if triggered, 2.75 * 4.8 = 6.93x the expected return for that game and pay table.

The following six tables show the number of combinations, probability and return for each hand by the number of cards held for 8-6 Bonus Poker Deluxe.

The following table is for 0 cards held. The probability of the feature is 30.24%. That makes the expected multiplier 1 + 0.3024*(6.93-1) = 2.793232.

### 0 Cards Held

Event Pays Combinations Probability Average
Multiplier
Return
Royal flush 800 1,588,620 0.000000 2.793232 0.000089
Straight flush 50 8,693,460 0.000000 2.793232 0.000030
Four of a kind 80 160,950,720 0.000008 2.793232 0.000902
Full house 8 993,777,120 0.000050 2.793232 0.000557
Flush 6 1,403,617,560 0.000070 2.793232 0.000590
Straight 4 2,675,274,000 0.000134 2.793232 0.000750
Three of a kind 3 14,739,155,760 0.000739 2.793232 0.003098
Two pair 1 33,594,719,760 0.001685 2.793232 0.002354
Jacks or better 1 113,077,238,400 0.005673 2.793232 0.007923
Loss 0 551,044,363,920 0.027645 2.793232 0.000000
Total   717,699,379,320 0.036005 0.000000 0.016293

The following table is for 1 card held. The probability of the feature is 25.03%. That makes the expected multiplier 1 + 0.2503*(6.93-1) = 2.484279.

### 1 Card Held

Event Pays Combinations Probability Average
Multiplier
Return
Royal flush 800 36,450,756 0.000002 2.484279 0.001817
Straight flush 50 61,994,820 0.000003 2.484279 0.000193
Four of a kind 80 2,008,777,680 0.000101 2.484279 0.010014
Full house 8 11,125,537,920 0.000558 2.484279 0.005546
Flush 6 15,029,740,464 0.000754 2.484279 0.005619
Straight 4 21,595,736,232 0.001083 2.484279 0.005383
Three of a kind 3 158,461,654,680 0.007950 2.484279 0.029624
Two pair 1 342,805,637,160 0.017198 2.484279 0.021362
Jacks or better 1 1,713,972,730,248 0.085986 2.484279 0.106806
Loss 0 4,625,202,334,140 0.232035 2.484279 0.000000
Total   6,890,300,594,100 0.345669 0.000000 0.186365

The following table is for 2 cards held. The probability of the feature is 19.43%. That makes the expected multiplier 1 + 0.1943*(6.93-1) = 2.152199.

### 2 Cards Held

Event Pays Combinations Probability Average
Multiplier
Return
Royal flush 800 84,004,800 0.000004 2.152199 0.003628
Straight flush 50 51,907,020 0.000003 2.152199 0.000140
Four of a kind 80 24,735,071,460 0.001241 2.152199 0.106826
Full house 8 91,717,184,196 0.004601 2.152199 0.039611
Flush 6 12,134,379,840 0.000609 2.152199 0.003930
Straight 4 7,221,069,636 0.000362 2.152199 0.001559
Three of a kind 3 1,035,705,361,944 0.051959 2.152199 0.167738
Two pair 1 1,475,954,482,464 0.074045 2.152199 0.079680
Jacks or better 1 2,625,262,032,888 0.131703 2.152199 0.141725
Loss 0 4,941,603,627,972 0.247908 2.152199 0.000000
Total   10,214,469,122,220 0.512434 0.000000 0.544838

The following table is for 3 cards held. The probability of the feature is 13.42%. That makes the expected multiplier 1 + 0.1342*(6.93-1) = 1.795806.

### 3 Cards Held

Event Pays Combinations Probability Average
Multiplier
Return
Royal flush 800 201,185,820 0.000010 1.795806 0.007250
Straight flush 50 309,313,620 0.000016 1.795806 0.000697
Four of a kind 80 19,143,558,720 0.000960 1.795806 0.068987
Full house 8 27,493,408,800 0.001379 1.795806 0.009908
Flush 6 11,842,378,020 0.000594 1.795806 0.003201
Straight 4 7,098,632,640 0.000356 1.795806 0.001279
Three of a kind 3 405,790,777,260 0.020358 1.795806 0.054837
Two pair 1 7,662,344,580 0.000384 1.795806 0.000345
Jacks or better 1 64,469,029,680 0.003234 1.795806 0.002904
Loss 0 217,221,939,000 0.010897 1.795806 0.000000
Total   761,232,568,140 0.038189 0.000000 0.149407

The following table is for 4 cards held. The probability of the feature is 6.95%. That makes the expected multiplier 1 + 0.0695*(6.93-1) = 1.412135.

### 4 Cards Held

Event Pays Combinations Probability Average
Multiplier
Return
Royal flush 800 152,741,160 0.000008 1.412135 0.004328
Straight flush 50 1,095,297,720 0.000055 1.412135 0.001940
Four of a kind 80 4,785,889,680 0.000240 1.412135 0.013562
Full house 8 37,221,845,760 0.001867 1.412135 0.010548
Flush 6 108,753,011,400 0.005456 1.412135 0.023113
Straight 4 40,860,218,520 0.002050 1.412135 0.005789
Three of a kind 3 - 0.000000 1.412135 0.000000
Two pair 1 400,134,841,920 0.020074 1.412135 0.014173
Jacks or better 1 54,886,948,380 0.002754 1.412135 0.001944
Loss 0 587,144,851,920 0.029456 1.412135 0.000000
Total   1,235,035,646,460 0.061959 0.000000 0.075398

There is no chance at the feature with five cards held. Therefore, the average multiplier is always 1.0.

### 5 Cards Held

Event Pays Combinations Probability Average
Multiplier
Return
Royal flush 800 30,678,780 0.000002 1.000000 0.000616
Straight flush 50 276,109,020 0.000014 1.000000 0.000346
Four of a kind 80 - 0.000000 1.000000 0.000000
Full house 8 - 0.000000 1.000000 0.000000
Flush 6 37,980,329,640 0.001905 1.000000 0.005716
Straight 4 76,206,089,520 0.003823 1.000000 0.007646
Three of a kind 3 - 0.000000 1.000000 0.000000
Two pair 1 - 0.000000 1.000000 0.000000
Jacks or better 1 - 0.000000 1.000000 0.000000
Loss 0 - 0.000000 1.000000 0.000000
Total   114,493,206,960 0.005744 0.000000 0.014324

The next table summarizes the probability and contribution to the return by number of cards held. The lower right cell shows a return of 98.66%.

### 5 Cards Held

Card Held Probability Average Win Return
0 0.036005 0.016293 0.452522 0.016293
1 0.345669 0.186365 0.539143 0.186365
2 0.512434 0.544838 1.063236 0.544838
3 0.038189 0.149407 3.912291 0.149407
4 0.061959 0.075398 1.216908 0.075398
5 0.005744 0.014324 2.493837 0.014324
Total 1.000000 0.986626 0.000000 0.986626

The next table summarizes the probability and contribution to the return by the winning hand. The "Average Win" is after extra hands and multipliers. The lower right cell shows a return of 98.66%.

### 5 Cards Held

Event Average Win Combinations Probability Return
Royal flush 1394.962220 506,649,936 0.000025 0.017728
Straight flush 73.983000 1,803,315,660 0.000090 0.003347
Four of a kind 157.077052 50,834,248,260 0.002550 0.200291
Full house 15.650672 168,551,753,796 0.008456 0.066170
Flush 8.983328 187,143,456,924 0.009389 0.042170
Straight 5.738711 155,657,020,548 0.007809 0.022407
Three of a kind 6.303223 1,614,696,949,644 0.081005 0.255297
Two pair 2.079867 2,260,152,025,884 0.113386 0.117914
Jacks or better 2.278644 4,571,667,979,596 0.229349 0.261302
Loss 0.000000 10,922,217,116,952 0.547940 0.000000
Total   19,933,230,517,200 1.000000 0.986626

The return for conventional 8-6 Bonus Poker Deluxe is 98.49%. That makes the additional return with the feature equal to 0.17%.

## Other Known Games

Here is a list of games and pay tables I saw at the \$0.25 denomination at the Rampart casino in Las Vegas.

• 7-5 Bonus Poker
• 8-6 Jacks or Better
• 8-6 Bonus Poker Deluxe
• 8-6 Double Bonus
• 9-6 Double Double Bonus
• 25-15-8-4-4-3 Deuces Wild
• 7-4-4-3 Deuces Wild Bonus