Ask the Slot Expert: A royal on Pick-a-Pair

Question: I was lucky enough to hit a Royal Flush on a 25-cent Pick-a-Pair machine. WOW!!

I was wondering if you could tell me what the odds were.

Answer: Wow, indeed.

For those not familiar with the game, here's a description. You are dealt two cards on the left side of the screen. Those two cards will be part of your final hand.

Two stacks of three cards are dealt on the right side of the screen. The topmost card of each stack is face up. You choose which stack you want to complete your hand based on the up-card.

The Wizard of Odds analyzed various Pick-a-Pair (aka Pick 'em Poker) paytables on this page.

Because this is much more of a stud game than a draw game, the hands pay more than similar paytables on draw poker machines. The royal flush, for instance, ranges from 6,000 to 10,000 coins for a five-coin bet in the paytables the Wizard analyzed. It's amazing how powerful the ability to replace any or all cards in your hand is.

The Wizard gives the same probability of landing a royal flush for each paytable he analyzed: 0.000003. Taking the reciprocal tells us that you'll get a royal flush once very 333,333 hands, on the average. And you thought royals were rare in draw poker!

The Wizard makes a couple of interesting points on the page. One is that you have only two choices, which stack do you want. In draw poker, you have 32 choices: keep or discard for each of five cards.

His second point is that even though the screen shows two cards face down in each stack, that situation is mathematically equivalent to dealing two cards at random from the deck after you choose the face-up card.

In fact, this may be how the machine actually works. Video poker machines used to select all 10 cards that might be needed for a hand when you pressed the Deal button. Cheats were able to reverse engineer the RNG function in some machines and they were able to determine the five cards that were waiting in the wings. They were then able to make a much better informed decision about which cards to hold or discard. They might have made a play that a regular player would never make like breaking a king-high straight flush because they knew that the ace they needed for the royal was waiting to replace the nine.

As a result, regulations were changed to require video poker machines to select only the cards needed for the initial hand when you press the Deal button and then to choose any cards needed to complete the hand when you press the Draw button, continually shuffling the deck while you make your decision.

If the machine sits with the face-down cards already selected while the player chooses the stack makes the machine vulnerable to RNG cheats, so I suspect that the program chooses two more cards at random from the deck after the player selects a stack. As the Wizard said, it's mathematically equivalent -- and much more secure.

Pick 'em Poker is sometimes very frustrating. A few times I had a pair in the two mandatory cards and the other two cards I needed for four-of-a-kind were the two optional cards. Impossible to get a quad on the play.

It never happened to me, but I can imagine someone getting very upset with this nightmare scenario: A suited king and ace in the mandatory cards -- so far so good -- and the jack and queen of the same suit for the two optional cards. Not only is a royal impossible, but also a straight flush.

It might seem like the strategy for Pick 'em Poker would be easier to learn than a draw poker strategy because you have fewer choices, but the strategies that the Wizard has on the page look pretty complicated to me. You can get similar long-term paybacks with simpler to play draw poker paytables. I think I'll stick with draw poker and just play Pick 'em for low stakes for fun every once in a while.