A closer look at reversible royals

Mar 1, 2004 11:23 PM

A very interesting derivative of Jacks or Better was introduced nearly 15 years ago, with the catchy name of Reversible Royals, or RR for short. Also known as "sequential royals," it’s probably coincidence, but RR originally got its start at our railroad (RR) motif casino, Palace Station.

The game offers a huge jackpot of 10,000 for 1 ($12,500 on a 5-quarter play) for a royal flush in sequence 10-J-Q-K-A or in exact reverse order A-K-Q-J-10, in any suite. It also offers a bonus payout on four-of-a-kinds; ranks 2-3-4 pay 40 for 1 while aces pay 870 for 1, all others remain at the standard 25 for 1. For these benefits, the payout on full house/Flush is cut to 6/5 in lieu of the 9/6 which full-pay machines feature.

Most players are conditioned to understand that when the pay schedules of conventional games are "adjusted," the gimmicking usually favors the house, in the long haul, by reducing the payback percentage. So, it is not surprising to find that is the case with RR. But, in the case of RR, the cost to the player is very small, indeed, considering the added volatility introduced by way of the mini-jackpot on four aces, together with that RR jackpot (a down payment on a house, maybe), the game should be attractive to serious players.

Let’s look at what the schedule changes imply, first assuming that the playing strategy (ranking) for full-pay Jack or Better is utilized. Since the royal flush is hit an average of once in 40,000 games only two of the possible 120 arrangements will be in the winning sequences, we can estimate that the big jackpot will be hit an average of once in 2,400,000 hands. While that may be discouraging, the extra 9,300 bet-units (10,000 minus 800) is worth 0.38 percent in overall payback.

To a very close approximation, four-of-a-kinds occur equally often in all ranks. With 80 for aces, 40 for the 2-3-4s and 25 for all others, the average payout on quads is worth 1.82 percent in payback, because those quads hit an average of once in 423 hands. To be exact however, we must reduce this figure to 1.62 percent to recognize that we frequently break up pairs of 2-3-4 ranks in pursuit of flushes, thereby causing few quads in these ranks.

Combining these two "pluses" gives us 2.0 percent, which is nearly equal to the 2.3 percent loss resulting from the 8/5 schedule. At this point we should consider what we might achieve by expert play in adjusting our strategy which causes a lower-value ranking to move up to a higher-value ranking will swing the payback percentage our way.

For example, in Jacks or Better, we play all pre-draw triplets like: 10C-JC-QC-QH-QS in that exact order, by holding the matching cards, simply because the Expected Value (EV) of the triplet is 4.3 whereas the EV of the three-card royal is only 1.4. In RR, the super-high jackpot makes the EV of this particular (sequential) three-card royal, which is a jackpot candidate, over 5.8. Accordingly, any triplet that includes a sequential three-card royal is played for the royal.

As another case, consider the hand: 10D-4D-QD-KD-7D, in that exact order. This would be a pat flush worth 6 in Jacks or Better but in RR it is worth only 5. Therefore it is expert strategy to play this as a three-card royal with its EV of 5.7.

Similar examples occur is straight and two-pair hands. With expert strategy for RR, we can virtually restore the payback to the 99.6 percent level we attain in full-pay Jacks or Better.