Posted by Wizard
Oct 19, 2020

## Introduction

In early October 2020 I heard of a reversible royal video poker game at the Red Rock casino in Las Vegas with an enormous jackpot. To be specific, it was a jackpot over \$40,000 for a 5¢ denomination game. This would be equivalent to a win of 160,000 for 1. Remember, one must make a five-coin bet to qualify for the progressive. A reversible royal pays for a sequential royal flush in either direction (10-J-Q-K-A) or (A-K-Q-J-10).

On October 17, 2020 I paid a visit to investigate. I did indeed find a bank of four games with the linked reversible royal jackpot. It is located near the Starbucks in the food court (not to be confused with the other Starbucks by the gift shop). At that date and time the jackpot was at \$40,389. There were six base games the player could choose from, all of which qualified for the jackpot, as follows. The return column shows the return without the reversible royal jackpot.

Game Pay Table Return
Bonus Poker Deluxe 6-5 95.36%
Jacks or Better 6-5 95.00%
Triple Double Bonus 7-5 94.92%
Double Double Bonus 6-5 94.66%
Double Bonus 8-5 94.19%
Bonus Poker 10-8-5-3-1 94.18%

As the table above shows, the highest return is on 6-5 Bonus Poker Deluxe at 95.36%.

A jackpot of \$40,389 for a 5-cent game is equivalent to a win of 147,722 for 1. Putting that and the rest of the pay table into the video poker analyzer at Wizard of Odds, results in the following return table.

Win Pays Permutations Probability Return
Reversible Royal Flush 807,782 67,567,248 0.000001 0.109525
Royal Flush 4,000 2,531,111,347 0.000025 0.020317
Straight Flush 250 10,545,248,235 0.000106 0.005290
Four of a Kind 400 246,151,065,684 0.002470 0.197580
Full House 30 811,309,337,868 0.008140 0.048842
Flush 25 1,067,259,148,415 0.010708 0.053542
Straight 20 1,275,953,861,466 0.012802 0.051209
Three of a Kind 15 7,722,917,814,918 0.077488 0.232464
Two Pair 5 10,770,132,885,066 0.108062 0.108062
Jacks or Better 5 22,463,692,195,905 0.225389 0.225389
All Other 0 55,295,592,349,848 0.554808 0.000000
Totals 99,666,152,586,000 1.000000 1.052220

The lower right cell in the table above shows a return of 105.22%. It should be emphasized that this return optimal strategy, including considering the order of the cards.

The image above is for the same jackpot on Triple Double Bonus.

My advice is if you have two or less cards are in position for a reversible royal, then don't muddy the waters with positional exceptions and play standard 6-5 Bonus Poker Deluxe strategy. That link will take you to the video poker strategy maker at Wizard of Odds for that game and pay table.

With three cards in position for a reversible royal, then follow the strategy for the same game, but with an average royal win of 3671. This is the weighted average of a 1.79% chance of getting a win of 161556 for a reversible royal and 98.21% chance of a regular royal win of 800. These wins are based on the total bet of 25 cents.

With four cards in position for a reversible royal, always go for the royal, even with a pat straight flush.

Assuming a playing speed of 1,000 hands per hour, the expected win of this play is \$13.05 per hour. This does not include the value of points or that the meter will continue to rise as you play. The probability of getting a reversible royal is 1 in 1,475,066 per hand. Assuming the same playing speed, playing 24 hours a day, on average a reversible royal will come along once every 61.5 days.

## Second Progressive

After this article was published, on October 20, 2020, a reader mentioned another 5¢ reversible royal game in the same casino with a \$73,844 jackpot. Later that day, I returned to the Red Rock to investigate. It can be found near the entrance by the buffet. The bad news is that this larger jackpot requires a 10-coin bet, as opposed to a 5-coin bet for the \$40,389 jackot. In other words, the ratio of the jackpot to bet amount is less. The ratio of jackpot to bet amount is 147,722. The good news is that the base pay tables were more generous. To be specific, the following table shows the base pay tables available and the return before considering the jackpot for a reversible royal.

Game Pay Table Return
Double Bonus 9-6-4 96.38%
Bonus Poker Deluxe 7-5 96.25%
Jacks or Better 7-5 96.15%
Double Double Bonus 7-5 95.71%
Triple Double Bonus 7-5 94.92%
Deuces Wild 25-15-10 94.82%
Bonus Poker 10-8-5-3-1 94.18%

The greatest return is that of 9-6-4 Double Bonus at 96.38%.

The next table shows the return for 9-6-4 Double Bonus with a reversible royal jackpot of 147,722 for 1. The lower right cell shows a return of 105.27%.

Win Pays Permutations Probability Return
Reversible Royal Flush 147,722 67,459,882 0.000001 0.099987
Royal Flush 800 2,495,093,079 0.000025 0.020028
Straight Flush 50 10,924,785,363 0.000110 0.005481
Four Aces 160 22,253,946,864 0.000223 0.035726
Four 2s, 3s, 4s 80 52,308,875,382 0.000525 0.041987
Four 5s thru Ks 50 161,090,857,086 0.001616 0.080815
Full House 9 1,067,274,737,292 0.010708 0.096376
Flush 6 1,111,860,442,001 0.011156 0.066935
Straight 4 1,261,479,363,060 0.012657 0.050628
Three of a Kind 3 7,402,211,583,588 0.074270 0.222810
Two Pair 1 12,095,167,336,452 0.121357 0.121357
Jacks or Better 1 20,990,003,172,849 0.210603 0.210603
All Other 0 55,489,014,933,102 0.556749 0.000000
Totals   99,666,152,586,000 1.000000 1.052733

While the return is close to the 5-coin game by Starbucks (105.27% vs. 105.22%), the expected win per hand is more than twice as much. To be specific, it is 2.63 cents per hand, compared to 1.31 cents per hand of the 5-coin game. Assuming a playing speed of 1,000 hands per hour, the expected win per hour is \$26.37. This game is also less volatile with a standard deviation of 121.66, compared to 133.14 of the five-coin game.

I should remind the reader that if you don't hit the reversible royal, the player can expect to lose \$14.33 per hour playing the 5-coin game and \$23.63 per hour playing the 10-coin game. There will also probably be a steep tax obligation on the jackpot, depending on how the winner does his taxes.

Mental Oct 20, 2020

The probability of getting a reversible royal is 1 in 1,475,066 per hand.[/q]

This probability assumes you make all optimal strategy changes. With optimal play, 40% of SRFs will come from holding two or fewer cards. With no strategy changes, less than 22% of SRFs come from holding two or fewer cards.

Any casual player would do well to just figure out and add in a few of the most critical 2-card SRF strategy changes.

Wizard Jan 30, 2021

As of January 30, 2021, the jackpot on the buffet bank was hit and the Starbucks bank is at \$41,492.70.