I've only given this about 2 min of thought, so tell me if I'm starting out on the wrong track ... my gut feeling is Frank's overthinking this a little too much.
I'd be inclined to solve for the number of hands of play for which the probability of filling the card is about 63.2% and presume this represents a card cycle.
(This value roughly represents the general likelihood of hitting any given hand at least once within one cycle of play for that hand. Obviously I'm assuming that the relation between hit probability and cycle carry over to consideration of multiple hit types, where you're looking for at least one hit of each type. I may be weak on this point ... I haven't investigated, by calculating a small scenario, to see if it holds true.)
I'd calculate that probability, most likely through trial and error for a various assumed number of hands, by calculating the respective hit probability for each individual hand included on the card over that number of hands and multiplying the results together.
No?
- H.
--- In vpFREE@yahoogroups.com, "Frank" <frank@...> wrote:
>
> I did some work on this before and came up with .2% as the card value.
>
> But they had gen 1, 2, 3 and 4 cards. And the return of each was different. I think gen 1 was 1.17%.
>
> I did not save the info or the math work. So here's a tip for calculating it yourself.
>
> When you are trying to hit things like a bingo card fill, that involve multiple overlapping cycles, you have to include the effect of standard deviation and waste into your equations.
>
> --- In vpFREE@yahoogroups.com, Vegasvpplayer <vegasvpplayer@> wrote:
> >
> > I've been trying to come with an average number of hands on 9/6 JoB or 8/5 BP to complete a Bingo card. The five hardest spots to fill are a royal flush and a straight flush in all 4 suits. I know the cycle for a RF is about 40k and a SF is about 10k. In the 40k royal cycle you will have an average of 4 SF's but probably not one in each of the 4 suits. My gut feeling is the normal cycle for all 4 suites of SF will be somewhere around 80k to 100k hands. Am I close?
> >
> > Sent from my iPhone
> >
>
