video poker--missing a royal flush by one card
June 2nd, 2011 at 6:27:54 PM
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What is the probability of missing a royal flush by one card in video poker? Put another way, with what frequency should one expect to miss a royal by one card? I recently played approximately 6,000 hands of 8/5 bonus poker and missed a royal by one card 18 times. I was surprised by the frequency. Is this in keeping with the probabilities?
June 2nd, 2011 at 6:31:56 PM
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June 2nd, 2011 at 6:39:21 PM
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Actually, I'm talking about missing a royal by one card after drawing. Getting 0-3 to a royal on the deal, and then ending up with 4 to a royal.
June 2nd, 2011 at 7:01:02 PM
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June 2nd, 2011 at 9:53:34 PM
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Yeah, it seems like you just missed but in reality it is pretty common. For example, if you were dealt 3 to a rf and and drew one out of the 2 rf cards you weren't that close because you had 2 opportunities to draw to 2 outs. By the rule of 4 in poker odds calculations, this is around an 8% chance. Drawing the royal flush however is like 0.1% I think.
June 3rd, 2011 at 1:26:25 AM
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Quote: clarkacalYeah, it seems like you just missed but in reality it is pretty common. For example, if you were dealt 3 to a rf and and drew one out of the 2 rf cards you weren't that close because you had 2 opportunities to draw to 2 outs. By the rule of 4 in poker odds calculations, this is around an 8% chance. Drawing the royal flush however is like 0.1% I think.
Yes. Starting with three to a royal and replacing two cards:
The odds to make a four to a royal: 2/47*45/46 + 45/47*2/46 = 0.083256
The odds to make a royal: 2/47*1/46 = 1 / 1081
Dividing the former by the latter we get 90, so in other words you are going to see 90 four-to-a-royal "near misses" until you get the real deal.
June 3rd, 2011 at 6:33:55 AM
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Thank you all for your replies. More specifically, though, what I'm seeking is the frequency with which one should expect to get four to a royal. For example, when playing 8/5 bonus poker, the frequency of a royal flush is once every 40,233 hands; a straight flush, once every 9,360; 4 aces, once every 5,106. What would the comparable number be for one card short of a royal flush?
June 5th, 2011 at 9:59:22 PM
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Quote: normandThank you all for your replies. More specifically, though, what I'm seeking is the frequency with which one should expect to get four to a royal. For example, when playing 8/5 bonus poker, the frequency of a royal flush is once every 40,233 hands; a straight flush, once every 9,360; 4 aces, once every 5,106. What would the comparable number be for one card short of a royal flush?
Why not just take that 40,000 number and divide by 90?
