Originally Posted by accountinquestion View Post
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.
The 2X multiplier used on one of Rob's five Royal Flushes (the 3X was used on another of them) don't have to be generated by jacks or better. For example, if you are dealt a scratch hand (holding nothing), you're final hand created from the replacement cards could be a pair of jacks or pair of queens or pair of kings or pair of aces. Any of which would generate a next hand 2X multiplier which would then have been used on one of Ron's dealt royal flushes. The scratch hand's replacement cards could generate any of the paying quad-kicker hands, a straight flush or royal flush - any of which would also generate a 2X multiplier. If you were dealt three to straight flush with three low cards and the two discarded cards were replaced by a high pair you would generate a 2X multipler for the next spin (the royal flush spin) - and on and on and on. So no,you would not, in fact, just need to figure the probabability of dealt jacks (which never improved in the ending hand otherwise a higher multiplier would get generated). The interested reader (which is to say no one) can go through all the other holds that could create a 2X multiplier for the next hand (all high card single card holds, all holds of a low card three of a kind that end up improving to a four of a kind with a kicker, etc. ). The interested reader would have to figure out the probability of getting each type of dealt hand hold that has the potential for its discard replacement cards to create a 2x next hand multiplier and then also calculate the probability of getting the proper (2x next hand multiplier) ending hand with that particular hold. There's quite a few combinations - a pat jacks or better that does not improve is but one of them.