All of the numbers on Michael Shackleford's chart are a max of 6 decimal
places. The probability of a RF on the redraw is 0.000000497. Rounded to 6
decimal places it is 0.<<
Assuming correct play, this figure can't be correct. While the odds of being dealt a royal--or any other combination for that matter-- can be computed, since no game-skill is required, the same is not true of the 47 remaining cards prior to deciding to hold nothing. For example, in 9/6 JOB you would never draw 5 if you had any paint (A,K,Q,or J) and there would also be fewer 10's since you'd keep them with suited royal combos, other than Ace, Ten. (Actually, you'd even keep suited A,10 when the progressive reached 5335 coins without a flush penalty, 5605 coins with a flush penalty in 9/6 JOB progressive.) Just like Gin (good players focus on every card played, so they're sure of the make-up of either the remaining deck or cards in opponent's hand), the correct answer would depend on the condition of the remaining deck (47 virtual cards)--there would definitely be a greater density of the 5 cards need for a royal than in the original 52. (By density I'm talking about a higher probability than 1:13--nobody can tell you the exact figure without more information.) You'd need to use a computer-generated algorithm from WinPoker (perfect play) to analyze the probability of each rank being one of the 47. As I said before, the figures would vary from game-to-game.
You will rarely have a hand where the correct play is to draw 5 and once more the odds of that happening vary from game-to-game. However, once the decision to draw all 5 has been made the odds of drawing a royal are better than 1 in 650,000. Nobody can give you an exact answer without making a grossly incorrect assumption--that all games are played the same resulting in uniform probabilities within the remaining deck.
Of course you'll get fewer 5-card draw royals overall since you'll seldom toss all 5--just like a person playing 5 million hands is more likely to get royals than one playing 5 hundred hands.
Linda Boyd
Author: "The Video Poker Edge"
www.squareonepublishers.com
Toll Free: 1-877-900-2665
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Best Tutorial Software: WinPoker
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