What might be, might be

16 October 2016

By John Grochowski

QUESTION: Playing Double Double Bonus Poker, I held 2-2, discarded a king, and the draw brought A-A-A. Boom! Boom! Boom!

I was happy with the full house, of course, but it got me wondering what would have happened if I had held the king instead. The way those aces popped up so fast, was the game ready to deal me a fourth ace if I only left it enough room to deal four cards?

ANSWER: If you held the king instead of the 2s, you might have gotten an entirely different draw. Your timing would have been different, and on most current machines, the remaining cards shuffle continuously until you hit the draw button.

However, let’s assume you would have received the same draw. After the first three aces came up on the draw, you had seen eight of the deck’s 52 cards. That leaves 44 unseen cards.

So after you have seen the first three aces, the chances of the next card being an ace are 1 in 44.

In the bigger picture, you made the right play. You don’t know those first three aces are coming until they’ve been dealt, so you have to play the percentages.

Dealt a hand with two 2s, a king and two throwaway cards such as a 5 and 9, holding 2-2 brings an average return of 4.38 coins. Holding the king and drawing four brings an average of 2.19 coins.

Holding 2-2 precludes the possibility of drawing four aces, as you demonstrated. However, four of a kind will show up on an average of 0.28% of draws – 45 possible quad combinations in 16,215 draws. All will be four-deuce hands, and a little more than a quarter of you quads will include a 3, 4 or ace kicker. That boosts the usual 400-coin payoff on four 2 to 800.

If you hold just the king, there are 53 possible four-of-kinds in 178,365 draws, or .003 percent of hands. Only one of those possible quads is four aces. Since the king precludes a low-card kicker as the fifth card, the aces pay the same 800 as those 2s with a kicker.

Hold 2-2 and you have a much better chance at four of a kind and much better chance at an 800-coin return on a big-paying quad.


QUESTION: On one of those new roulette tables with the video betting, it was pretty cool. I could touch the screen and get a stats page that told me a lot more than the usual number boards with the 18 most recent numbers. It had all these stats and graphs showing the percentages numbers had come up for thousands of spins. It broke out hot numbers and cold numbers in recent spins, and it gave percentages on combinations, too, like red or black and the columns.

It was all pretty cool to look at, but with so much information I was kind of overwhelmed, too.

Is there any way to boil it down to useful data? What’s the best way to use the information?

ANSWER: The best way to use the information provided at electronic roulette tables is for entertainment. There is no predictive value to any the information provided on stats displays.
It doesn’t matter if the display tells you that in the last 1,000 spins, 28 has turned up 3.2% of the time and 14 has turned up only 1.9%.

On the next spin, every number has a 1 in 38 chance of occurring. Odds are unchanging, past is past, and in roulette, the past is no guide to the future.