How Much Does a Royal Flush Count?

15 November 2014

By Jerry Stickman

Most serious video poker players, even those who only play casually once or twice a year, know how much their favorite video poker machine pays with expert play. While they may not know to the second decimal place, they know that generally the games pay as follows.

• Full pay (9/6 – 9 for 1 for a full house, 6 for 1 for a flush) Jacks or Better pays 99.54 percent of the money played.

• Full pay (8/5) Bonus Poker pays 99.16 percent.

• Full pay Deuces Wild (25/15/9/5/3/2 -- 25 – wild royal, 15 – five of a kind, 9 – straight flush, 5 – four of a kind, 3 – full house, 2 – flush) pays 100.76 percent.

• Not So Ugly Deuces (NSUD: 25/16/10/4/4/3 -- 25 – wild royal, 16 – five of a kind, 10 – straight flush, 4 – four of a kind, 4 – full house, 3 – flush) pays 99.73 percent.

• Full pay (10/7 – 10 for 1 for a full house, 7 for 1 for a flush) Double Bonus pays 100.17 percent.

• 9/7 Double Bonus pays 99.11 percent.

All of the games listed above have very good payback schedules. Some of them even give the player an advantage over the house.

A payback of 99.54 percent means that over the long run the player will lose only 46 cents for every 100 dollars played through the machine. A 99.73 percent payback will only cost the player 23 cents for every 100 dollars played over the long run. A 100.17 percent payback will actually pay the player 17 cents for every 100 dollars played. And a payback of 100.76 percent pays the player 76 cents for every 100 dollars played over the long run.

These are very small house edges. It seems that a player should be able to play for days on a bankroll of a couple of hundred dollars. Why, then do we typically feed in bill after bill when playing our favorite game?

One reason is the inherent volatility or variance of the game. The wins and losses do not come in a nice steady stream. Instead, there may be several losses, then a small win, then several more losses, maybe a moderate win, then several more losses, and so on. The edge of the game is not applied in a nice constant slope. Instead, it is a roller coaster ride.

The other reason, which is also related to volatility, is the fact that a royal flush counts for such a large amount of the payback. When playing the maximum of five credits, a royal pays 800 for 1. Using expert strategy while playing the games mentioned above the player will get a royal flush once every roughly 40,000 to roughly 48,000 hands depending on the game being played. This means for better than 40,000 hands the player will not have the benefit of a royal flush to push the payback up to the long term average.

How much does this affect the payback? Let’s take a look.

Jacks or Better produces one royal every 40,390 hands in the long run with expert play. The payout for this royal amounts to 1.98 percent of the total payback for Jacks or Better. This means that between royals the house advantage for full pay Jacks or Better is not 99.54 percent but 1.98 percent less than that or 97.56 percent. Rather than losing only 46 cents per 100 dollars played, the player loses $2.44 per 100 dollars played. This is a major drop in payback – one that dramatically reduces the player’s bankroll.

The hourly loss while playing at a fairly leisurely 600 hands per hour amounts to $18.30 for the quarter player and $73.20 for the dollar player.

Bonus Poker produces one royal every 40,233 hands and amounts to 1.99 percent of the total payback. Rather than a house edge of 84 cents per 100 dollars, the house edge between royals jumps to $2.83 per 100 dollars played. At 600 hands per hour the hourly loss is $21.23 for a quarter player and $84.90 for a dollar player.

Full pay Deuces Wild produces one royal every 45,282 hands and amounts to 1.77 percent of the total payback. Rather than a player edge of 76 cents per 100 dollars played the house edge between royals is $1.01 per 100 dollars played. At 600 hands per hour the hourly loss is $7.58 for a quarter player and $30.30 for a dollar player.

Not So Ugly Deuces (NSUD) produces one royal every 43,456 hands and amounts to 1.84 percent of the total payback. Rather than a house edge of 27 cents per 100 dollars played, the house edge between royals becomes $2.11 per 100 dollars played. The hourly loss at 600 hands per hour is $15.83 for a quarter player and $63.30 for a dollar player.

Full pay Double Bonus (10/7) produces one royal every 48,048 hands with a 1.67 percent contribution to the total payback. Between royals, rather than a player edge of 17 cents per 100 dollars played, there is a house edge of $1.50 per 100 dollars played. At 600 hands per hour the quarter player can expect to lose $11.25 with a dollar player losing $45.

Finally, 9/7 Double Bonus produces one royal every 48,035 hands with a 1.67 percent contribution to the total payback. Between royals the house edge goes from 89 cents per 100 dollars to $2.56 per 100 dollars played. The hourly loss rates at 600 hands per hour are $19.20 for the quarter player and $76.80 for the dollar player.

As you can see, the royal flush is a major contributor – in fact it is the major contributor – in almost every game. If you aren’t getting royals, you are hemorrhaging cash to the casino.
Most players are aware of this just by watching the bills being fed into the machine, but the numbers above show exactly how much the royals actually mean. Be aware of this and plan your bankroll accordingly.

May all your wins be swift and large and all your losses slow and tiny.