JorB Royal Flush Odds

Just curious as to what the true odds are for getting a RF in JorB when you play perfect strategy vs. when you play just to optimize your chances for a RF (e.g. you are playing in a tournament).

For example, in perfect strategy (which optimizes your expectation) you would always throw away a two card suited royal in favor of a small pair. However, in playing a strategy optimized for a RF, you would always throw away four of a kind in favor of drawing a RF, no matter how remote the chance may be.

I answered that once in an Ask the Wizard column. From memory, the probability was about 1 in 20,000-25,000.

From halfway down this page.

Quote:

I was curious. How do the odds change in video poker if a person always shoots for a natural royal flush? (In other words always holding the most beneficial hadn to obtain a natural royal flush.... disregarding all other possible hands.)

A strategy of going for a royal at all costs, as if all the other hands paid zero, would result in a return of 47.85% on a 9/6 Jacks or Better game. The expected frequency of a royal would increase form once every 40388 hands to once every 23081

Thanks miplet. According to the reference, the exact answer is:

Once in 40388 hands [optimal strategy] to once every 23081 hands [RF only strategy]