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20 May 2013
By Alan Krigman
Question: Video poker and at least two table games have jackpots for royal flushes. What are the odds against pulling such a hand?
Answer: At the tables, jackpots are paid for royal flushes in Caribbean Stud and Let It Ride. In both cases, players get five cards with no discards or draws. The odds are therefore identical in the two games and are 649,739-to-1. This is figured by determining that 52 cards can be combined into 5-card hands in 2,598,960 different ways. Of these, only four are royal flushes. The probability is therefore 4/2,598,960, which equals 1/649,740. This means one way to win out of 649,740 total hands. Expressed as odds, it's 649,739 losses to every win.
The chances are different at video poker for several reasons. For instance, after you see your five initial cards, you can hold some and replace the rest; this means you can form the royal flush from as few as five cards to as many as 10. There's also an element of choice in that you could break a low pair and hold a single picture, sacrificing "expected win" but leaving open the chance of a royal. And, of course, the odds depend on details such as wild cards. Here are some typical values, based on playing strategies which maximize expected win.
13 May 2013Question: Blackjack "card counters" increase their bets when they determine that shoes are rich in 10s. Assuming players bet only on single spots, why is this situation advantageous? Don't players and dealers have equal chances of receiving high hands in these circumstances? Answer: The advantage in ... (read more)
6 May 2013Question: At blackjack, you might split pairs, then double down on one or more of the hands when the dealer has an ace or 10 showing. This means you might have multiple bets on the table. If the dealer doesn’t check in advance for a blackjack and ends up getting one, you only lose some of this. How much do ... (read more)
29 April 2013Question: Most slot machines now seem to have "bill acceptors" or take coupons so you don't have to get rolls or cups of coins to get started or to continue if you run out. Someone told me if you play with bills, you'll lose more because the machine assumes you have more money to keep going. Is this true? ... (read more)