Odds on Reversible Royals

26 June 2022

By John Grochowski

QUESTION: I have a question about the progressive Reversible Royals video poker machines. I just returned from Vegas and I noticed quite a few of these games in mostly quarter denominations with monster payoffs for the reversible royal. I'm talking about $50,000-$60,000.

Are the odds of drawing a reversible royal or being dealt one much greater than the normal 1 in 40 thousand hands? I would imagine with the size of the payouts it has been a really long time before anyone hit one.

ANSWER: In Reversible Royals, the usual payback with five credits wagered is 50,000 credits if the royal is on screen in the 10-J-Q-K-A or A-K-Q-J-10. If the royal flush cards are in any other order, you get the usual 4,000-credit jackpot.

There are 120 different card orders for any royal flush. Only two fit the reversible pattern, so reversible royals are 60 times rarer than royals in which card order doesn't matter.

If no strategy adjustments are made to account for card position on the initial deal, a game that yields a royal once per 40,000 hands would yield a reversible royal once per 2.4 million hands.

Michael Shackelford has a page on Reversible Royals at wizardofodds.com. He calculates that if adjustments were made, you'd see a reversible royal about once per 1.9 million hands.

One additional point: Frequency of royals differs by game and strategy. In 9-6 Jacks or Better, expert strategy will bring a royal an average of 1 in 40,391 hands, but figures rise to 1 in 40,799 in 9-6 Double Double Bonus Poker, 1 in 43,423 in 25-15-9-4-4 Deuces Wild and 1 in 48,035 in 9-7-5 Double Bonus Poker.

Cards are dealt in the same proportions, but our strategies differ to optimize payoffs, so proportions of final hands differ.



QUESTION: When you play Hundred Play or 50 Play video poker are there 100 or 50 individual random number generators running or not? Many times when dealt two pair there are no full houses which seems very unlikely and I've become skeptical!

ANSWER: To the best of my information, a single random number is used, but with up to 100 separate draws. If you're playing 50 hands and hold a pair of 9s, a pair of 5s and discard a 10, the RNG selects a number that corresponds to one of the other 47 cards for hand No. 1, selects a number from that full 47-card set for hand No. 2, and so on.

The RNG does not retain knowledge of what it gave you from one hand to the next. If the result of the first hand was that you stayed on a two-pair payoff, chances remain 4 in 47 that you'll draw a full house on hand No. 2, or No. 3, and so on.

The odds are exactly the same if 50 or 100 separate RNGs are used to select numbers corresponding to cards in 47-card sets -- the original 52 minus the five you received on the deal. On each hand, you have a 4 in 47 chance of completing a full house. Among the remaining 47 cards, four would complete a full house -- the other two matching each pair.

In an average draw, you'd see a fraction more than four full houses in a 50-hand play, but you are an underdog for a full house in each individual hand. Frequent draws with no full houses are normal. Those draws are balanced by times you draw more than four full houses -- sometimes many more -- in your 50 hands.