See if this sounds right on how to figure odds on games where order
matters, like sequential royals.
First, to compare to games where order does NOT matter, the way to
figure odds (EV) for any hand is to count up the number of possible
hands of each type, multiply by the value of each hand, and then
divide by the number of possible hands, which depends on the number
of cards drawn (52-card deck numbers used here).
Draw 1 47 possible hands
Draw 2 47*46/2 = 1081
Draw 3 47*46*45/2/3 = 16,215
Draw 4 47*46*45*44/2/3/4 = 178,365
The divisor above is the term that takes care of duplicates in a
different order, so when order DOES matter, all you have to change in
the above method is to get rid of the divisor. Your new constants are:
Draw 1 47 (same)
Draw 2 47*46 = 2062
Draw 3 47*46*45 = 97,290
Draw 4 47*46*45*44 = 4,280,760
So, to determine when you should alter strategy in a sequential royal
game, you should start with determining the excess royal value over
bet (the portion above 800:1 in most cases), and then divide this
amount by the above numbers. Let's consider two examples, one where
the SR pays 10,000-to-1, and another where the SR is a high
progressive like one I have locally, currently paying 39,460-to-1.
Examples 10K SRF Prog SRF
Excess royal value per bet 9,200 38,660
Draw 1 add-on 195.745 822.553
Draw 2 add-on 4.255 17.882
Draw 3 add-on 0.095 0.397
Draw 4 add-on 0.002 0.009
(note these values are per bet to convert to 5-coin values,
multiply by 5)
Thus, a 3-card-royal with all 3 cards in the correct position is
worth, in 10K SRF JOB, 1.575 + 4.255 = 5.830, or more than a pat
straight and more than 4-to-a-SF and more than most 3OAKs. In my
progressive game, a 2-card-royal beats a low pair. In both games, a 4-
card-royal properly positioned is worth much more than a pat SF, so
if you are dealt TJQK9 in any suit, you should throw away the 9. Even
the 4-card-draw number, small as it is, could change strategy
slightly as in a few cases it may be better to hold a single face
card, properly positioned, over 2 unsuited face cards.