Royal Flush on Wizard of Odds
Two Flushes
Two Straights
Two One Pair Jacks or Better
One Loss.
Very lucky draw. The straights were only three times more probable than a Royal Flush.
Quote: technicsI didn’t even notice the second Royal until this morning! Now I just need to do it in real life!!😀
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"Dang, how good is this paytable?"
Quote: Dieter"Dang, how good is this paytable?"
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Am I missing something? It looks like a straightforward 9/6 JoB to me.
Quote: WizardI was going to calculate the probability of getting 2 royals, 3 flushes, 2 straights and 2 high pairs on the draw, but I need to know which card was discarded.
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Can't we just assume it was an off-suit 2-T?
Quote: WizardI was going to calculate the probability of getting 2 royals, 3 flushes, 2 straights and 2 high pairs on the draw, but I need to know which card was discarded.
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Can't we just assume it was an off-suit 2-T?
Seems the RNG is not acting much like an RNG.Quote: WizardI was going to calculate the probability of getting 2 royals, 3 flushes, 2 straights and 2 high pairs on the draw, but I need to know which card was discarded.
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Quote: ThatDonGuyQuote: Dieter"Dang, how good is this paytable?"
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Am I missing something? It looks like a straightforward 9/6 JoB to me.
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Getting an 8140 coin payout on one royal flush would be a splendid paytable.
Quote: DieterQuote: ThatDonGuyQuote: Dieter"Dang, how good is this paytable?"
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Am I missing something? It looks like a straightforward 9/6 JoB to me.
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Getting an 8140 coin payout on one royal flush would be a splendid paytable.
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8140 on a bet of 50 is hardly "splendid"
Quote: ThatDonGuyQuote: DieterQuote: ThatDonGuyQuote: Dieter"Dang, how good is this paytable?"
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Am I missing something? It looks like a straightforward 9/6 JoB to me.
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Getting an 8140 coin payout on one royal flush would be a splendid paytable.
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8140 on a bet of 50 is hardly "splendid"
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Fair enough. My comment was intended as friendly mockery of not noticing the second royal until the morning after.
Thank goodness for screenshots.
Quote: gordonm888Quote: WizardI was going to calculate the probability of getting 2 royals, 3 flushes, 2 straights and 2 high pairs on the draw, but I need to know which card was discarded.
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Can't we just assume it was an off-suit 2-T?
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Would you have held a suited low card?
Quote: billryanQuote: gordonm888Quote: WizardI was going to calculate the probability of getting 2 royals, 3 flushes, 2 straights and 2 high pairs on the draw, but I need to know which card was discarded.
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Can't we just assume it was an off-suit 2-T?
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Would you have held a suited low card?
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Quick math:
Assuming a Royal pays 800, a straight pays 4, a high pair pays 1, and a flush pays some value F:
Discarding a suited low card to go for the Royal pays (800 + 8 x F + 3 x 4 + 9 x 1) / 47 = (821 + 8 F) / 47
Holding the flush pays 47 F / 47, which is the better play if 47 F > 821 + 8 F, which is true when F >= 22.
Somehow, I don't see anybody offering a game that pays 22 for a flush.
From the picture, we can see 12 cards out of the 52, so the discard had to be one of the other 40. If we presume optimal play, any one of those 40 cards would have been discarded.Quote: WizardI was going to calculate the probability of getting 2 royals, 3 flushes, 2 straights and 2 high pairs on the draw, but I need to know which card was discarded.
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If it was one of the 6 remaining flush cards, the probability would be 9.7035e-06; one of the 7 remaining Aces, Kings, or Jacks, it would have been 1.14446e-05; if it was the remaining Queen, the probability would have been 6.43757e-06; if it had been one of the 26 two thru ten off-suit cards, the probability "grows" to 1.39481e-05.
We have no reason to believe that any one of those 40 cards was more likely than any other. So, taking a weighted average of the 40 possibilities seems reasonable and leaves us with a probability of 1.26855e-05, or integer odds of 78,829 to 1.
There are "only" 1001 combinations of results possible (distributing the ten hands among the 5 possible results), so this is a fairly unlikely combination. However, the combined probabilities of combinations with at least two royal flushes is less than 0.0182, so maybe this exact mix is not that rare among what we might call "postworthy" combinations; perhaps somewhere around rank 403rd most likely out of the 1001 possibilities.
Happy New Year!
Sorry, no idea what the discard was.
Anyone know many times has a ten hand draw has produced two royals on the Wizards 0f Odds site?
What are the odds that one ten hand draw would produce two royals?
Quote: technicsThanks everyone.
Sorry, no idea what the discard was.
Anyone know many times has a ten hand draw has produced two royals on the Wizards 0f Odds site?
What are the odds that one ten hand draw would produce two royals?
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Before the draw the odds of getting two royals playing optimal strategy at 9-6 Jacks or Better on any one play is 151,630 to 1. 93.66% of two-royal hands are produced from drawing to a dealt 4-card royal.
The probability of getting two royals on a draw after a dealt hand like the one you posted is 0.01715 or odds of 57.305 to 1.
