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# A wild streak indeed!

21 September 2014

QUESTION: Something very unusual happened at the casino recently. Playing my usual Double Double Bonus machines, I was dealt three 4s. Of course, I didn’t get the other 4. On the very next round, I was dealt three 4s again. And again I didn’t get the other 4. Imagine my shock when I’m dealt another three 4s – and of course I didn’t get the other 4. I know about the RNGs, but what are the odds of getting nine 4s in three consecutive rounds. What do you think about this scenario?

ANSWER: The odds against being dealt three fours three hands in a row are very long indeed. To see just how long, you need to start with the distribution of hands in five-card stud poker – nearly all video poker is draw poker, but your pre-draw hand is the equivalent of a stud hand, just five cards dealt out of the 52.

There are 2,598,960 possible hands in which card order doesn’t matter. Of those, 54,912 are three of a kind. And because there are 13 card denominations, one of every 13 three-of-a-kinds are three 4s, leaving 4,224 possible three-4 hands. Divide all possible hands by the number of hands that include three 4s, and you get 615. Your chances of being dealt three 4s on any one hand are 1 in 615.

For the chances of it happening three times in a row, multiply 615x615x615. There is a 1 in 232,608,375 chance – and yes, that’s 232 million.

That seems very unlikely, and it is. However, millions of hands of video poker are played in casinos every day, and the unlikely will happen as a matter of course. You just happened to be in the right place at the right time to see it.

As for failing to draw the fourth 4 three hands in a row, that’s par for the course. After you’ve seen your first five cards, there are 47 remaining in the deck. If you hold just the three 4s and draw two cards, you have two chances in 47 to draw the final 4, which we can reduce to 1 in 23.5.

That means there are 22.5 chances in 23.5 that you will NOT draw the fourth 4. Given three hands with three 4s, there is an 87.77 percent chance that you will miss on all three.

QUESTION: I need you to explain something about Blackjack Switch. I was playing for the first time, and I had one hand with Ace-5 and one hand with 10-6. I figured I could switch the 5 and the 10, and have Ace-10 in one hand, and 5-6 for another. That would give me a blackjack and a double-down hand.

But when I signaled to switch, the dealer did it different. He switched the Ace and the 10, so now I had 10-5 and Ace-6 – really not much help at all. I told him that wasn’t the switch I wanted, but he said those were the only two cards I could switch. I could go back to the original I wanted, but I could only switch the Ace and 10.

A little while later, a woman was dealt a similar hand, and she was allowed to switch to get a blackjack. I was getting a little steamed, so I just left after that hand. What do you think was going on?

ANSWER: Most likely everything was done correctly, but you just didn’t get an adequate explanation from the dealer.

You’re permitted to switch only the second cards in each hand. You probably were dealt 5 first and Ace second in one hand, and 6 first and 10 second in the other. With that card order, the only cards you can switch are the Ace and the 10. That’s what the dealer should have explained, that only the second cards can be switched.

When the other player got her hand, no doubt the card order worked so she could switch to create a blackjack.
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John Grochowski

John Grochowski is the best-selling author of The Craps Answer Book, The Slot Machine Answer Book and The Video Poker Answer Book. His weekly column is syndicated to newspapers and Web sites, and he contributes to many of the major magazines and newspapers in the gaming field, including Midwest Gaming and Travel, Slot Manager, Casino Journal, Strictly Slots and Casino Player.

Listen to John Grochowski's "Casino Answer Man" tips Tuesday through Friday at 5:18 p.m. on WLS-AM (890) in Chicago. Look for John Grochowski on Facebook and Twitter @GrochowskiJ.