Objective proof?

[accountinquestion]

To generate the 2x and 3x multipliers that Ron cashed his dealt royal flush on, it would be helpful to know what the dealt hand was on Ron's previous spin before the dealt royal flush spin. To generate the 2x multiplier, the ending hand of the spin before the dealt royal flush spin, would need to be a jacks or better pair, quads not consisting of rank 5 to King (kicker or not), a straight flush or a royal flush. To generate the 3x multiplier, the ending hand of the spin before the dealt royal flush spin would need to be two pair or quads of rank 5 to King. So there are a very large number of possibilities of what Ron was dealt on the spin before the dealt royal flush spin, that could generate a 2x and a 3x multiplier. The question then is what is the probability of getting exactly one 3X multiplier and exactly one 2x multiplier on the previous spin. I'm not interesting in going through the combinatorics of all the dealt hands that could lead to the 2x and 3x multiplier that two of Ron's five dealt Royals were used on. BTW, it is not at least one 2x and not a least one 3x multiplier, but exactly one of each, so the odds are a lot longer than 5x on the shot as you defined it. Also pat hands have nothing to do with the calculation of the probability of this shot, only the ending hand. If you get dealt a pair of jacks plus rags, you are holding the jacks. If they don't improve you get a 2x multiplier otherwise it could be a better multiplier available for the next spin. But many many other holds (for example you hold an Ace and get another Ace plus rags) besides a pair of jacks could get you a 2x multiplier to be cashed in on by one of Ron's royal flushes on the ensuing deal - again I am not going to go through all of the possible holds that could generate these multipliers.

I'll be honest, I just glanced at the picture originally and thought it was 2x every hand from previous round. Odds are actually far closer to a pat royal. So my math wasn't that off, just my memory of what was in the picture he posted was way off. If every hand has 2x multiplier then that'd almost always be a pat hand on the previous one. I was deserving of your snark.

Also when I define a longshot, I don't typically use the exact frequency on something like this but I'd use the floor of the odds of what happened (if that makes sense). Being dealt straights etc would also count as they'd be even better than 2x. When I was thinking it was 2x, all you need to do is basically figure out what the odds of pat jacks of better are and go from there. When it isn't a pat hand, then it becomes far far more difficult and truly not worth spending time on - like you've suggested.

If I was trying to figure out the likelihood of something like this happening, I would never try and calculate the exact odds of this specific instance. I'd instead try to calculate that it takes to get a 5x or higher total multiplier. That'd include 6x-30x totals. Seems like a better way to reference the improbability of something like this happening.