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Last Updated: January 25, 2023

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Fortune X Poker

Introduction

Fortune X Poker is a video poker variant that awards randomly bonuses. If the bonus is awarded, the player may either keep a hand with one multiplier or decline it for a higher multiplier the next hand. As usual, the player must an additional fee to invoke the feature.

Rules

The following rules are based on those found at VideoPoker.com.

  1. The game is played as an optional feature on top of convention 3-, 5-, or 10-play video poker.
  2. If the player bets 1 to 5 coins per play, then the rules are the same as conventional multi-play video poker.
  3. If the player bets 10 coins per play, then the player will be eligible to play the bonus feature. With the feature active, wins are based on 5 coins bet per play, with the other 5 coins per play acting as a fee for the feature. The rest of the rules apply only when the feature is enabled.
  4. The feature will be triggered on the deal with a specified probability. All I know is this probability is 11% for 9-6 Double Double Bonus (despite the rule screens claiming it is 10.96%.
  5. Immediately after the feature is enabled, the player may either accept a 2x multiplier for that hand or decline it.
  6. To decline a multiplier, the player doesn't have to do anything. The game defaults to rejecting all multipliers except 12x. To accept a multiplier, the player should click the box in the lower right of the screen showing the multiplier.
  7. If the player declines a multiplier, the hand the player makes a full bet on will have a larger multiplier.
  8. The progression of multipliers goes 2x, 3x, 5x, 8x, 12x.
  9. If the player gets to the 12x multiplier, it is automatically accepted.
  10. If the player leaves the game, or switches to a different game, with a multiplier available for the next hand, then the next player to play the game will be eligible for it.

If these rules were unclear, here are the rule screen directly from the game.

Example

 

In the image above, the feature was awarded.  My choices were to keep the 2x multiplier with a low pair on the deal or decline it.  I chose to decline it, playing out the hand normally.  I held the pair of nines, which developed into one two pair, paying 10, on the draw (not shown).

In the previous hand I declined the 2x multiplier, so this time I'm eligible for a 3x mutliplier.  With only an outside straight draw on the deal, I chose to decline the mutliplier.  After the draw, two of the hands improved to a straight (not shown) for a win of 2×20 = 40.  

The next hand, I was dealt a pair of nines on the deal.  The multiplier is now at the 5x stage.  A low pair is not enough to accept the multiplier, so I declined it.  My low pair improved to a two pair and a three of a kind (not shown), for a win of 5+15=20.  

 

 

In the following hand, I was dealt a pair of eights on the deal.  I am now at the fourth stage of the multiplier progression, at 8x.  Like the previous hand, a low pair is not enough to keep the multiplier, so I declined it.  My low pair improved to two three of a kinds (now shown), for a win of 2×15 = 30.
 

The fifth and final hand in the progression has a 12x multiplier.  My hand on the deal was a pair of aces.  

 

My pair of aces improved to two high pairs (each paying 5), one two pair (paying 5), and two three of a kinds (each paying 15) on the draw.  With the 12x multiplier, my win is 12×(2×5 + 5 + 2×15) = 12×45 = 540. 

Strategy

I show the player should be indifferent to accepting a multiplier at the following expected values on the deal, based on 9-6 Double Double Bonus. These expected values are based on a single-coin bet (for example the EV of a dealt royal flush is 800). If the actual expected value is higher, accept the multiplier, if lower, decline it.

  • 2X multiplier: Indifferent EV = 8.901087
  • 3X multiplier: Indifferent EV = 4.889740
  • 5X multiplier: Indifferent EV = 2.567263
  • 8X multiplier: Indifferent EV = 1.411099

For games other than 9-6 Double Double Bonus, the breakeven points should still be about the same, but not exactly.

Analysis

The following table shows my analysis for 9-6 Double Double Bonus. As a reminder, the return for this game in conventional video poker is 98.98%. The probability of triggering the feature, when not already in it, is 11%. The table below shows the probability of every combination of hand and multiplier. The return column is the produce of the base win, multiplier, probability and 0.5. The reason for dividing by 2 is the player must double his bet to invoke the feature. The lower right cell shows a return with the feature of 99.01%.

9-6 Double Double Bonus Detailed Analysis

Hand Multiplier Base Win Probability Return
Royal flush 12 800 0.000001 0.006861
Straight flush 12 50 0.000006 0.001918
Four aces + 2-4 12 400 0.000004 0.008621
Four 2-4 + A-4 12 160 0.000008 0.008017
Four aces + 5-K 12 160 0.000010 0.009718
Four 2-4 12 80 0.000022 0.010761
Four 5-K 12 50 0.000095 0.028521
Full house 12 9 0.000633 0.034201
Flush 12 6 0.000662 0.023847
Straight 12 4 0.000745 0.017868
Three of a kind 12 3 0.004389 0.079009
Two pair 12 1 0.007177 0.043062
Jacks or better 12 1 0.012324 0.073945
Nothing 12 0 0.032241 0.000000
Royal flush 8 800 0.000001 0.003024
Straight flush 8 50 0.000005 0.001024
Four aces + 2-4 8 400 0.000004 0.006418
Four 2-4 + A-4 8 160 0.000006 0.003614
Four aces + 5-K 8 160 0.000011 0.007032
Four 2-4 8 80 0.000014 0.004416
Four 5-K 8 50 0.000078 0.015643
Full house 8 9 0.000551 0.019818
Flush 8 6 0.000180 0.004327
Straight 8 4 0.000309 0.004943
Three of a kind 8 3 0.002566 0.030791
Two pair 8 1 0.004346 0.017383
Jacks or better 8 1 0.007294 0.029176
Nothing 8 0 0.000291 0.000000
Royal flush 5 800 0.000001 0.001403
Straight flush 5 50 0.000002 0.000311
Four aces + 2-4 5 400 0.000002 0.002029
Four 2-4 + A-4 5 160 0.000006 0.002327
Four aces + 5-K 5 160 0.000005 0.002004
Four 2-4 5 80 0.000014 0.002844
Four 5-K 5 50 0.000060 0.007513
Full house 5 9 0.000200 0.004504
Flush 5 6 0.000154 0.002314
Straight 5 4 0.000303 0.003030
Three of a kind 5 3 0.001451 0.010883
Two pair 5 1 0.000000 0.000000
Jacks or better 5 1 0.000006 0.000016
Nothing 5 0 0.000035 0.000000
Royal flush 3 800 0.000001 0.000863
Straight flush 3 50 0.000001 0.000090
Four aces + 2-4 3 400 0.000002 0.001249
Four 2-4 + A-4 3 160 0.000006 0.001432
Four aces + 5-K 3 160 0.000005 0.001233
Four 2-4 3 80 0.000015 0.001750
Four 5-K 3 50 0.000062 0.004624
Full house 3 9 0.000205 0.002772
Flush 3 6 0.000154 0.001382
Straight 3 4 0.000002 0.000013
Three of a kind 3 3 0.001488 0.006698
Two pair 3 1 0.000000 0.000000
Jacks or better 3 1 0.000006 0.000008
Nothing 3 0 0.000015 0.000000
Royal flush 2 800 0.000001 0.000578
Straight flush 2 50 0.000001 0.000060
Four aces + 2-4 2 400 0.000002 0.000836
Four 2-4 + A-4 2 160 0.000002 0.000307
Four aces + 5-K 2 160 0.000005 0.000825
Four 2-4 2 80 0.000002 0.000194
Four 5-K 2 50 0.000013 0.000652
Full house 2 9 0.000113 0.001014
Flush 2 6 0.000005 0.000028
Straight 2 4 0.000002 0.000008
Three of a kind 2 3 0.000122 0.000366
Two pair 2 1 0.000000 0.000000
Jacks or better 2 1 0.000006 0.000006
Nothing 2 0 0.000015 0.000000
Royal flush 1 800 0.000020 0.007997
Straight flush 1 50 0.000093 0.002330
Four aces + 2-4 1 400 0.000048 0.009558
Four 2-4 + A-4 1 160 0.000115 0.009240
Four aces + 5-K 1 160 0.000137 0.010973
Four 2-4 1 80 0.000317 0.012678
Four 5-K 1 50 0.001322 0.033052
Full house 1 9 0.009158 0.041211
Flush 1 6 0.010203 0.030610
Straight 1 4 0.011406 0.022811
Three of a kind 1 3 0.065248 0.097873
Two pair 1 1 0.111541 0.055770
Jacks or better 1 1 0.191687 0.095843
Nothing 1 0 0.520239 0.000000
Total     1.000000 0.990069

The following table summarizes the possible events in 9-6 Double Double Bonus, without the hand breakdowns. Again, the lower right corner should a return of 99.01%.

9-6 Double Double Bonus Summary Analysis

Game State Probability Average
Base Win
Multiplier Return
Game not in feature 0.634851 0.989808 1 0.314190
2X multiplier accepted 0.000289 16.872652 2 0.004874
2X multiplier rejected 0.078176 0.931120 1 0.036396
3X multiplier accepted 0.001961 7.516250 3 0.022114
3X multiplier rejected 0.076214 0.821845 1 0.031318
5X multiplier accepted 0.002240 6.995312 5 0.039177
5X multiplier rejected 0.073974 0.807941 1 0.029883
8X multiplier accepted 0.015655 2.357209 8 0.147607
8X multiplier rejected 0.058319 0.622751 1 0.018159
12X multiplier 0.058319 0.989808 12 0.346350
Total 1.000000 0.990069

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