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Xtra Card
Introduction
Xtra Card is a variant of video poker developed by Aristocrat. It can be accessed as an additional feature in single-play and triple-play video poker formats. By wagering ten credits per game, players gain opportunities for extra hands and multipliers. This game is available on multi-game devices labeled as \"Winners World Multi-Game\" and \"Storming Jackpots\" at the top of the screen. Additionally, it can be played on bartop gaming machines.
Rules
- This game builds on the concept of single-play for three-play video poker, which I presume the audience is already familiar with.
- When a player bets between 1 to 5 credits for each game, it functions as traditional video poker.
- By wagering ten credits per round, players can activate the feature. In this case, winnings will be calculated based on a baseline of five credits per game, while the extra amount bet acts as a non-refundable fee for a chance to access the feature.
- With a wager of 10 credits per round, there’s a chance to activate the feature depending on the cards a player holds, with exact probabilities that may vary between different games. Here’s an illustration using 8-6 Bonus Poker Deluxe:
- 0 cards held = 30.24%
- 1 card held = 25.03%
- 2 cards held = 19.43%
- 3 cards held = 13.42%
- 4 cards held = 6.95%
- 5 cards held = 0.00%
- Should the feature activate, players will receive one or two additional hands. The likelihood of receiving one additional hand is 25%, while the chance of getting two is 75%.
- When the feature is activated, both the original and the additional hands possess a 40% probability of having a multiplier attached.
- Available multipliers range from 2x to 10x, with the average multiplier being approximately 4.8.
Example
In the illustration provided, a player made a single bet. After securing a pair of queens, they were awarded two additional hands along with a 5x multiplier. One of these three hands improved to three of a kind, while the remaining two stayed as a high pair. The total payout was calculated as 5×(5 + 5 + 15) = 75.
Analysis
Upon activation of the feature, the average chance for one extra hand stands at 25% whereas for two it is 75%. Consequently, the mean total number of hands (including the original hand) is computed as 1 + (0.25*2 + 0.75*3) = 2.75.
Factoring in the 40% chance for an average multiplier of 4.8, the overall average multiplier (including 1x for no multiplier) becomes 0.6*1 + 0.4*4.8 = 2.52.
This leads to an anticipated value of the feature, once activated, as 2.75 * 4.8 = 6.93 times the expected return for that particular game and pay table.
The six tables below represent the combinations, probabilities, and returns for each hand based on the number of cards held in 8-6 Bonus Poker Deluxe.
The table summarizing outcomes for holding 0 cards shows a feature probability of 30.24%. This establishes the expected multiplier at 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 table for holding a single card indicates a feature probability of 25.03%, leading to an expected multiplier of 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 |
For two held cards, the feature probability stands at 19.43%, resulting in an expected multiplier of 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 feature probability for three held cards is 13.42%, which sets the expected multiplier at 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 |
When holding four cards, the feature probability drops to 6.95%, leading to an expected multiplier of 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 |
With five cards held, there are no opportunities to trigger the feature, so the average multiplier will consistently be 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 subsequent table consolidates the probability and average contribution to returns based on the number of cards held, indicating a return of 98.66% in the lower right cell.
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 |
Another table encapsulates probability and return contributions based on the winning hand, with the \"Average Win\" showcasing totals after accounting for additional hands and multipliers, again yielding 98.66% in the lower right.
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 conventional return for 8-6 Bonus Poker Deluxe is measured at 98.49%, which signifies the additional gain from the feature amounts to 0.17%.
Other Known Games
Here’s a compilation of games and pay tables that caught my eye at the $0.25 stake level in the Rampart casino located 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
External Links
Conversational threads surrounding Xtra Card can be found in my discussion forum at Wizard of Vegas .