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Best of Mark Pilarski
Deal Me In: One card short of good fortune27 May 2016
Here is the arithmetic, Larry.
With four different suits and five ways of catching the missing card, you multiply that by the remaining 47 cards that cannot complete your royal (4 x 5 x 47 = 940). As a result, there are 940 ways of being dealt four cards of a royal.
With 2,598,960 five-card hand possibilities, your chances are 940 in 2,598,960, which makes for odds of 1 in 2,764 of being dealt four cards of a royal.
I do not know your skill level, Larry, but I do know that the average number of hands played per hour for a seasoned veteran runs anywhere between 700-1,000.
Assuming, Larry, that you can play 700 hands per hour – a speed few can attain – it will take you 3.94 hours to play those 2,764 hands.
However, most players do not play in the 700 hands per hour range. Most are closer to 200. Consequently, at that rate, it will take 13.82 hours to play those same 2,764 hands.
The problem with these averages – in mathematics and statistics it’s called the “arithmetic mean” – is just that they are averages. All it means is that on any given hand, over the long run, there is a one in 2,764 chance you will initially draw a four-to-a-royal hand. Your three prospects, Larry, just came a tad bit faster than the odds say they should have.
By the way, Larry, as for hitting one of those elusive royals, typically, the odds of hitting one are about 40,000:1, but that varies from game to game, along with how you play your initially dealt cards. If you were playing Jacks or Better or Bonus Poker, it would be as mentioned above. On a Joker Poker machine, it is around 42,000:1; Deuces Wild, 45,000:1, and 48,000:1 on a Double Bonus Poker machine.
Dear Mark: You recently mentioned the game Let It Ride. The casino where my wife and I play also offers the game. I will stick to your advice and won’t be playing, but is there any chance you can briefly describe the game for us Neophytes? Ron W.
Let It Ride is a variation of five-card stud poker where you would wager on a poker hand that consists of three cards in your hand and two dealer community cards.
Play begins after each player makes three separate wagers of an equal denomination in spaces labeled (1), (2) and ($). The dealer then deals each player three cards, with two additional community cards dealt face down. After seeing their first three cards, players each have the option of pulling back their first bet, or, as the game is applicably named, declaring “let it ride.”
After the dealer then exposes one of the two community cards, each player has the option to remove the second bet or, once again, "let it ride," regardless of the first decision. Finally, the second community card is exposed. Losing bets not meeting the payout criteria are collected, and the winning wagers are paid, based on the ranking of the players’ hands and a payout schedule. Typically, a Royal Flush pays 1,000:1; a Straight Flush 200:1; Four-of-a-Kind 50:1; Full House 11:1; Flush 8:1; Straight 5:1; Three-of-a-Kind 3:1; Two Pair 2:1; and a pair of 10s or better 1:1.
Gambling Wisdom of the Week: “At home all day playing cards.” – George Washington, Diary, (September 5, 1770)
Best of Mark Pilarski