Repeat of the Same Hand

27 May 2021

By John Grochowski

QUESTION: I had something weird happen at Three Card Poker. I was dealt 5 of clubs, 10 of diamonds and 9 of clubs two hands in a row.

It’s bad hand, one I folded right away the first time. The second time, I looked at my cards and said, “Hey, these are the same cards as last time. Were they shuffled at all?”

The dealer pointed out that not only were they shuffled, they were a different deck since one deck is in the shuffler while the other was being dealt.

Other players were asking if I was sure they were the same cards. There’s no discard tray you can check
things like that, but I knew they were the same. Nobody else would have noticed since it wasn’t a
winning hand. They just had to take my word for it.

I was certain, and I’m wondering what the odds of that were. Is that something that happens all the time on ordinary bad hands and we just don’t notice, or was this as weird as it struck me?

ANSWER: Your hands were as unusual as you think. Consecutive hands with the same cards are rare regardless of whether they form a winning combination.

In single-deck games, every hand is unique. Assuming card order doesn’t matter -- and it doesn’t in the poker-based games we play in casinos -- there is only one hand consisting of 5 of clubs, 10 of diamonds and 9 of clubs, just as there is only one hand consisting of Ace of diamonds, King of diamonds and Queen of diamonds.

There are 22,100 possible hands in which card order doesn’t matter. You have a 1 in 22,100 shot at
being dealt any three specific cards, including the three you were dealt. The chance of being dealt three specific cards two hands in a row is 1 in (22,100 x 22,100), or 488,410,000.

Once you have seen the first three-card hand, the question becomes “what are the chances of receiving these three cards again?” The answer is 1 in 22,100, the same as seeing any three specific cards in any one hand.


QUESTION: I was paging through some old magazines and found an article you wrote that dismissed video slots as not real gambling. I find that outrageous. When I play video slots, I am betting real money. When I win, I am winning real money, and when I lose, I am losing real money.

How can you say I am not really gambling?

ANSWER: I remember the article. If I recall correctly, it was for Strictly Slots magazine, and I may also have used parts of it in a column here.

You have misunderstood what it said. It was a collection of comments from three-reel slot players talking what they liked about mechanical reels and didn’t like about video slots. A couple of them said they liked three-reel slots because the emphasis was on winning and losing, that there were paybacks on fewer spins but every paying spin returned several times your bet.

They didn’t care for video slot emphasis on entertainment or winners that return less money than you
wager.

Note this was all reader opinion. I did not comment. That is what I do when I compile columns of reader comments about what they like or don’t on games, unusual things they’ve seen at the tables, customer service glitches or any of the things players love to share and discuss. I let them have their say.

I agree wagers, wins and losses are as real on video slots as on other games, but I am not going to shout down those who disagree.