Righting a small wrong

22 May 2016

By John Grochowski

I do my best to answer questions from readers as they come in, although I will admit some get lost in the shuffle during particularly busy times.

Once in a while, the answer I give does not match the question the reader really had in mind.
Such was the case a short time ago when a woman drew a royal flush when playing nickel video poker.

She wanted to know if she’d still have drawn the royal if she was playing for quarters or dollars.

That’s one of the most frequent questions I get, and I try to answer it once or twice a year for readers who are just joining the party. I gave her the usual answer: The random number generator runs continuously, and very fast. Just the time taken to touch the screen and change the game setup from nickels to quarters or dollars would have been enough that her outcomes probably would have been different.

I e-mailed the reader an answer at the same time I was sending my editors the Q-A that used her question. Less than an hour later, she wrote to tell me she had a different question in mind.

“I meant, are the odds the same on video poker playing nickels, quarters or dollars?

“It seems I get more royal flushes on nickels, which I assumed the casino doesn't have to pay out as much that way.”

That’s an entirely different matter. I explained to her that the odds of drawing royal flushes change only with your strategy, not with the coin denomination. Nickel games do not deal more royals than quarter games.

Random number generators are programmed the same way for video poker games, regardless if whether you’re playing for nickels, quarters, dollars or any other denomination. In fact, on many multidenomination machines, the same RNG is used regardless of which coin denomination you’re playing.

All the RNG does is generate numbers that correspond with cards. Those numbers are applied in such a way that every card has an equal chance of appearing on every hand. Odds of drawing any given hand are the same as if a physical deck were in play.

That’s why we can calculate payback percentages on video poker games. Given a specific strategy, we know how often each hand will occur over a very long time.

In most casinos, nickel games pay less than quarter games because pay tables tend to be lower. I was in a casino recently that had games at 5, 10 and 25 cents on one back of machines, and 25 cents, 50 cents and $1 on another bank. The first bank had 7-5 pay tables on Double Double Bonus Poker on the 5- and 10-cent games, but 8-5 on the 25-cent game. The second had 8/5 on the 25- and 50-cent games, but 9/6 on the $1 games.

Royal flush frequency varies slightly on those games, at 1 per 40,799 hands at the 9/6 pay table, 1 per 40,066 at 8/5 and 1 per 39,639 hands at 7-5, but that’s because our strategy changes with the pay table, not because the cards are dealt differently.

If the casino put a 7/5 pay table on a dollar game, I wouldn’t play because the expected return with optimal play is only 95.71%, compared to 98.98% with a 9/6 pay table. But those who did play could expect a royal once per 39,639 hands, the same as on nickels with that pay table.

Casinos change payback percentages on video poker games by changing the pay tables, not by changing the frequency of big winners.

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