> I just realized the dealt RF cycle is different for each game type on
> Dream card because the frequency of the Dream card is not the same for all games.
yes. to get a dealt royal in DC, you need RF4 in the first four cards,
and then you need either the DC feature to activate, or you need to
spike that fifth card to the royal without it.
odds of RF4 in the first four cards is 20/combin(52,4) = 1/13536.25,
as you correctly computed.
odds of getting the dealt royal given the RF4 in the first four cards
depends on the DC frequency, which we'll call X. if DC activates, with
X probability, you're done. if DC doesn't activate, with probability
1-X, then you need the fifth card to be one specific card out of 48
for the royal. so the total is X + (1-X)/48.
odds of the dealt royal is the product of these two, and the cycle is
the inverse of the odds, so combin(52,4)/(20*(X + (1-X)/48)). for
various games, using the DC frequency given by Shackleford, we get:
DW 59.0% 22615
JoB 50.5% 26268
BP 46.7% 28312
DB 33.7% 38585
BDlx 31.3% 41356
DDB 31.0% 41730
TDB 26.7% 47955
i wonder if the variance on DC DDB might actually be *lower* than the
variance on DC JoB, because the dealt-royal cycle is so much longer.
that would be amusing. i don't really care enough to compute it
myself, though.
cheers,
five
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