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by John Grochowski

John Grochowski is a blackjack expert and a well-known and respected casino gambling columnist. His syndicated casino gambling column appears in the Denver Post, Casino City Times, and other newspapers and web sites. Grochowski has written six books on gambling including the "Answer Man" series of books ( He offers one-minute gambling tips on radio station WLS-AM (890) and podcasts are available at your question to Grochowski at

Q. My father-in-law and I were talking about insurance (blackjack), and how you win more hands if you take the insurance but win more money if you don't.

Are there other games besides blackjack where you choose to make plays that win less often because they win more money?

A. Video poker certainly qualifies. One example is the choice between holding a low par or a high card. Holding the high card will bring more winners because of the frequency of high pairs. But you'll win more money if you hold the low pair.

Let's use 9-6 Double Double Bonus Poker as an example, assuming a five-coin bet and with a starting hand of 6-6-7-9-King.

If we hold just the King, there are 178,365 possible draws, and 118,540 of them will bring no return.

Of the winners:

  • 45,324 will be pairs of Jacks or Better paying five coins for your five-coin bet
  • 9,033 will be two pairs paying five
  • 4,177 will be three of a kind paying 15
  • 446 will be straights paying 20
  • 493 will be flushes paying 30
  • 297 will be full houses paying 45
  • 49 will be four 5s through Kings paying 250
  • three will be four 2s, 3s or 4s paying 400
  • one will be four Aces paying 800
  • one will be a King-high straight flush paying 250 and
  • \one will be a royal flush paying 4,000.

Overall, you'll win on 33.5 percent of hands and the average payback per hand, including all the losers, will be 2.2 coins.

What if you hold the 6s instead?

  • Then there are 16,125 possible draws, with 11,559 losers.
  • Of the winners, there are 2,592 two-pair hands
  • 1,854 three of a kinds
  • 165 full houses and
  • 45 flushes.

The presence of two 5s precludes high pairs without it turning into two pairs, and there are no straights, flushes, straight flushes or royals.

You win on only 28.3 percent of the draws, but your average return rises to 3.7 coins.

The high card vs. low pair situation is one of the most important in video poker because it occurs so often. Just as with declining insurance in blackjack, players who get the most out of the game choose the play that wins less often.

Q. Playing online, I found a weird game called Mini-Roulette. It has one zero along with numbers 1 through 12. What's the house edge? Do you think we'll ever see it in live casinos?

A. I'd never heard of the game, so I searched and found Michael Shackelford's analysis at

Winning bets pay

  • 11-1 on single numbers
  • 5-1 on two-number splits
  • 3-1 on three-number bets that include rows as well as 0-1-2 and 0-2-3
  • 2-1 on four-number columns or corners and
  • even money on red, black, odd, even, 1 through 6, 4 through 9 or 7 through 12.

In addition, you get half your losing bet back if the ball lands on 0.

That last bit is important. It means the house edge is less on bets that don't include 0. House edges are 3.85 percent on all bets that don't include 0 and 7.69 percent on those that do.

I would not expect to see live-action versions of this game come to brick-and-mortar casinos. Properly balanced wheels are expensive to build and maintain, and it seems like Mini-Roulette would just draw customers from existing roulette tables rather than create new business. The game's best shot at a breakthrough in live casinos would seem to be inclusion on multi-game electronic tables.

Q. I got three-of-a-kind two hands in a row in Three Card Poker. It was pretty exciting. I was betting $5 on Pair Plus, so at 30-1, I won $150 on the first time. Then I raised the bet to $10 and won $300 the second time. That's all in addition to wining ante-play against the dealer, too, and getting the 4-1 ante bonuses there.

I have a couple of questions about it. What are the odds of two three of a kinds in a row? How would that compare to two straight flushes in a row? While we're at it, how about two in a row in some other games - two blackjacks in a row, two of the same number in a row in roulette, two royals in a row in Caribbean Stud?

A. You'll see three-of-a-kind at Three Card Poker an average of once per 425 hands. To find the probability of two in a row, you need to square that: 425 times 425 is 180,625. So your two in a row was a 1 in 180,625 shot.

That's a long shot, but long shots happen in casinos every day. There are so many wagers made that things that seem improbable are not only possible, but inevitable.

For comparisons to other wagers, we follow the same formula - find the chances of the event happening once, then multiply that chance by itself.

In Three Card Poker, straight flushes make up 1/460th of all possible hands, so your chance of a straight flush on any given hand is 1 in 460. For two in a row, it's 1 in 211,460.

Blackjacks are much more frequent at about 1 per 21 hands. The chance of two in a row is about 1 in 441 - narrow enough that you see consecutive blackjacks often. On double-zero roulette, each number is 1 of 38. The chance of the same number turning up twice in a row is 1 in 1,444.

With Caribbean Stud, we enter the world of extreme rarity. Caribbean Stud is a five-card stud game, and the chance of a royal per hand is 1 in 649,740. That puts two in a row at 1 in 422,162,067,600 - that's 422 billion and then some.

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