lottoarchitect wrote: "By the way, 4if4of8 means nothing, you need 4 parameters to define a wheel."
Which is why I wrote: "a 7-ticket wheel for 4-if-4-of-8 for a 6-draw lottery".
The "4-if-4-of-8" notation is derived from the terminology described in this forum under the title "What's a Lottery Wheel" at the "Lottery Wheel" link. So I thought it might be better understood than the algebraic notation (8,6,4,4)=7.
lottoarchitect wrote: "Given a covering v,k,t,m=b, [.... for] your 4if8, given it is a t < m construction [...]".
Actually, I wrote 4-if-4-of-8. And as I understand the (v,k,t,m)=b notation [1], that is a t=m construction.
That is a small detail. I mention it only to clarify my next question.
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In fact, I do not understand the t < m condition per se. Can someone explain it?
Consider the very excellent step-by-step explanation of the JADELottery algorithm starting at www.lotterypost.com/thread/228056/2017518, referenced by a Ramijami in an earlier response in this discussion.
The JADELottery example is for (9,5,3,4)=b. That is, a wheel that "guarantees" a 3-win if 4 of 9 match 5 drawn. It appears that b=5.
I don't exactly gronk the implications of the requirement "3 if 4 ...".
With "4 if 4 of 8", that is (8,6,4,4)=b, I believe that means the wheel of pick-6 tickets must cover all of the 70 4-tuples from the pool of 8 numbers.
But with "3 if 4 of 9", that is (9,5,3,4)=b, it seems that must mean the wheel of pick-5 tickets covers only some of the 126 4-tuples from the pool of 9 numbers.
Is that right?!
I'd be surprised if it is because that does not seem to "guarantee" as 3-win if (any of) 4 of the 9 numbers match part of the pick-5 drawing.
But if the requirement were different -- if (9,5,3,4) means that all of the 4-tuples must be covered by the wheel -- that would "guarantee" a 4-win. So why bother with (also) "guaranteeing" a 3-win?
If I'm wrong, I would appreciate it someone would post some counter-examples, namely: a (9,5,4,4) wheel, a (9,5,3,4) wheel, and a (9,5,3,3) wheel.
Unfortunately, the JADELottery explanation is not sufficient because the resulting 5-ticket wheel does not cover all 3-tuples or all 4-tuples.
So it does not seem to "guarantee" a 3-win at all, as I (mis?)understand the wheel requirements.
(Note: I have not yet worked through all of the JADELottery details to see if perhaps there is a minor typo that misrepresents the final wheel.)
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[1] I am familiar with the notation (n,k,t,m)=b used by an apparently different "Lotto Architect". This forum's silly rules do not permit me, a "new" member, to post a URL. Google for "lottery wheel terminology", and look for "anastasios tampakis" in the URL.
For that notation, n = #numbers to wheel (aka "pool"); k = #numbers drawn (aka "ticket size"); t = minimum "guaranteed" win (aka "prize category"); m = #numbers that must match (are among) the drawn numbers; and b = #tickets to purchase (aka "wheel").
In other words, a b-ticket wheel that guarantees a t-win if m of n match k drawn numbers.
A Google search also finds the notation (v,k,t,m)=b, with the same interpretation of the common variables, and v = n.