Mike asked about JoB and WinPoker:
Example.......if I put in A clubs, King clubs, 10 clubs, 4 clubs, and 7 hearts......Winpoker shows the 4 card flush to be much higher than the 3 card royal..... with the 4 card flush earning 1.27 coin return to 0.77 coin return for the 3 card royal. It comes up this way with most any different 3 card royal cards....
I know I have to be missing something simple here. Can anyone set me straight????
You are running your analysis with one-coin bet --- giving you 250-for-1 for a royal flush. At that royal payout, 4-card flushes are more valuable than 3-card royals.
If you switch to betting 5 coins, you'll see the 'usual' situation where 3-card royals are superior to 4-card flushes --- except for a few exceptions.
If you follow the exception guide given by AP you'll do WORSE than always holding the 3-card royal over the 4-card flush. Starting with AKT2 suited, holding AKT2 creates a 5.09 cent mistake (for a 5-coin dollar player) 21 times --- i.e. with any 3, 4, 5, 6, 7, 8, or 9 not of the same suit as the AKT2.
On the three times the fifth card is another T, AP's rule is correct by 0.46 cents
On the six times the fifth card is an unsuited J or Q, AP's rule is correct by 3.70 cents.
In the 30 possible fifth cards that are considered from that position, AP's play loses 2.78 cents on average every time. He is correct that it is simple to memorize. He is not correct that it is a good idea to memorize it. (If you play 9/6 DDB, for example, AP's rule works perfectly there --- but not for 9/6 JoB)
Bob