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Fortune X Poker
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.
The following rules are based on those found at VideoPoker.com.
- The game is played as an optional feature on top of convention 3-, 5-, or 10-play video poker.
- If the player bets 1 to 5 coins per play, then the rules are the same as conventional multi-play video poker.
- 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.
- 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%.
- Immediately after the feature is enabled, the player may either accept a 2x multiplier for that hand or decline it.
- 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.
- If the player declines a multiplier, the hand the player makes a full bet on will have a larger multiplier.
- The progression of multipliers goes 2x, 3x, 5x, 8x, 12x.
- If the player gets to the 12x multiplier, it is automatically accepted.
- 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.
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.
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.
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
|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|
|Three of a kind||12||3||0.004389||0.079009|
|Jacks or better||12||1||0.012324||0.073945|
|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|
|Three of a kind||8||3||0.002566||0.030791|
|Jacks or better||8||1||0.007294||0.029176|
|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|
|Three of a kind||5||3||0.001451||0.010883|
|Jacks or better||5||1||0.000006||0.000016|
|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|
|Three of a kind||3||3||0.001488||0.006698|
|Jacks or better||3||1||0.000006||0.000008|
|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|
|Three of a kind||2||3||0.000122||0.000366|
|Jacks or better||2||1||0.000006||0.000006|
|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|
|Three of a kind||1||3||0.065248||0.097873|
|Jacks or better||1||1||0.191687||0.095843|
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 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|
- Play Fortune X Poker for fun at VideoPoker.com.
- Discussion about Fortune X Poker in my forum at Wizard of Vegas.
Written by: Michael Shackleford