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Gaming Guru
VP Strategy and Hand Frequency26 November 2020
That's something I've explained often to players who wonder why royal flushes come up more often on one game than another. Given optimal strategy, you'll see a royal an average of once per 40,391 hands in 9-6 Jacks or Better but only once per 48,035 in 9-7-5 Double Bonus Poker. The reason is that our drawing strategy differs according to the pay table. That applies not only to royal flushes, but to all hands. Your strategy affects hand frequency. Let's look at a two examples to see how that works:
That affects frequencies of paying hands. The Double Bonus hold means you'll never draw a royal on that hand, while in Jacks or Better you'll hit the royal jackpot once per 1,081 times you make the two-card draw. The trade off is that in Double Bonus, you'll complete a flush once per 5.22 hands, while in Jacks or Better it's only once per 30.89. Other hands are affected, too, but you get the idea. The way we play that hand is part of why we draw fewer royals in 9-7-5 Double Bonus.
Why? Jacks or Better pays 2-for-1 on two pairs while DDB pays only 1-for-1. That enhances the value of the redraw in JB and depresses it in DDB. Double Bonus gives us extra incentive to make the inside straight draw by paying 5-for-1 on straights. The value of a redraw remains low at 1.64 coins per five wagered while drawing to the inside straight brings a 2;13-coin average, higher than any play on this hand on the other games. In DDB and DDB, the one-card draw brings a straight an average once per 11.75 hands. In JB, where we discard all five cards, then draw a straight once per 255.61 hands. The strategy difference factors into the frequency of straights overall. In JB, optimal play for the full game brings a straight once per 89.05 coins. That rises to once per 79.33 in DDB and once per 66.57 in DB. The cards we're dealt and draw remain random results. The machine isn't doing anything to change card frequency. We're the ones changing frequency of winning hands, and we're doing it through our draw decisions. Look for John Grochowski on Facebook (http://tinyurl.com/7lzdt44) and Twitter (@GrochowskiJ). This article is provided by the Frank Scoblete Network. Melissa A. Kaplan is the network's managing editor. If you would like to use this article on your website, please contact Casino City Press, the exclusive web syndication outlet for the Frank Scoblete Network. To contact Frank, please e-mail him at fscobe@optonline.net. Recent Articles
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