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
If I did the math right, you have a 51.27% chance of having a straight flush in each suit after 7 straight flushes.
--- 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
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.
Not being related to progressives, I'd have to think about it for a long time to give you the exact formula, but I can put the question to some of my mathy friends, this coming Thursday and see if they have something already.
No need to reinvent the wheel. Expect a post on Friday.
~FK
--- 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
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
>
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote: 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 over-thinking this a little too much.
Me over-thinking something. You are guilty of picking the low hanging fruit. That's like saying, I'm being "Frank" with you. Guilty as charged, but I thought over-thinking was my job.
I was working on a method that adds the reciprocals of all the probabilities, and then adds variance, based on the number of elements using something akin to the Poisson distribution.
I won't post it until it is flawless, and confirmed by multiple other sources.
~FK
yes, you're close.
obviously it'll take an average of one SF cycle to hit your first SF.
after you've hit your first, 1/4 of your SFs are going to be in the
same suit as the first one. so it'll take on average 1/(1-1/4) = 4/3
SF cycles to hit a second one in a new suit.
after you've hit two, 1/2 of your SFs are going to be in a suit you've
already hit, so it'll take on average 2 SF cycles to hit a third one
in a new suit.
after you've hit three, 3/4 of your SFs are going to be in a suit
you've already hit, so it'll take on average 4 SF cycles to complete
the set.
so, to get all four SFs, it'll take 1 + 4/3 + 2 + 4 ~= 8.33 SF cycles,
or about 75000 hands on average.
as for the average number of hands to fill out a card... you can use
your intuition and figure you'll probably but not certainly have the
royal within 75000 hands, and the quads certainly won't hold you up,
and bump it up to 85000 or so. or you can pull out your poisson
distributions and numerical integration and come up with a figure
of... 85000 or so. either way.
the promo stopped being interesting when they added the specific-suit
straight flushes. it was pretty monstrous on multiline quarters for
the first week.
cheers,
five
On Mon, Jan 3, 2011 at 9:02 AM, Vegasvpplayer <vegasvpplayer@gmail.com> 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?
I made a post on this but it got lost in cyberspace. I'll try again.
This is how I would have to do it on the straight flushes. SF chances at 9/6 Jacks is 9148.37, Bonus Poker is 9360 so no question 9/6 is the better play. I don't know anything about poisson or any of that stuff. I just know how this idiot country boy has to do it.
9/6 Jacks....no strategy shifts....I don't think I would use a strategy shift for a hand I'm gonna hit anyway if I play long enough.
It's obvious that the first cycle is 9148.37.
After that I would multiply 9148.37 times 4 which = 36,593.48. Then I would divide 36,593.48 by 3 which is 12,197.83 (represents the three remaining suits)and that would be the second cycle.
Then I would divide 36,593.48 by 2 which = 18,296.74 and this would be the third cycle.
36,593.48 would be the fourth cycle.
.........9,148.37
........12,197.83
........18,296.74
........36,593.48
TOTAL 76,236.42
--- 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.