gilbert_616 wrote:
Talk about the "sacrificed coins" in holding the 3-card RF and if you
play say 700-800 hands per hour, how many times (on average) would
you get the dealt 3-card RF in an hour play?
I happened to hit many royals from holding 3 cards but now, wondering
if it was worth it!? (now I'm confused :<)
Very approximately, you're dealt 3RF once every 65 hands (I'm still
feeling a little lazy and I'm not calculating the actual value). So,
we'll call it 10-12 times an hour, on average.
I don't know that "Was it worth it?" (concerning a 3RF hold over a HP)
is a useful question.
You take a certain risk and if it pays off, that's good ... if it
doesn't, that's unfortunate. The deed is done and "was it worth it?"
is a question more suited to philosophers than gamblers. A gambler
asks what'll they do next time.
Jean points us in a good direction with a suggestion to look to Frugal
VP for the math on this one. While I previously gave a limited peak
at the numbers with the example of holding suited JQK (the most
valuable 3 RF) over a high pair, FVP allows us to skip some cumbersome
arithmetic and still talk of the general situation you originally
raised: holding any 3 card RF over a high pair.
FVP indicates that shifting strategy so that 3RF is held over a high
pair in 9/6 Jacks reduces ER by .0703%.
The RF cycle is reduced from 39724.4 hands to 34375.9. Consequently,
for every 255316 hands played, you expect to gain 1 addition RF in
play. However, because of the overall reduced expected return, you
look to give up 4897 coins on other winning hands, for a net reduction
in win over that time of 897 coins.
As I suggested before, if you get a sufficient thrill from going for
the royal more often that the tradeoff makes sense for you, then it
can be said that this is a smart strategy move for you. But to
continue to go for it for no other reason than you have done well with
the hold previously isn't sound logic (although not quite as poor as
taking a second shot with a half loaded gun held to your head because
you got lucky with the prior shot ;).
- Harry