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Author	Topic: Looking for Reiterative Solution
David Roberts Member	posted January 16, 2005 04:49 PM <He seems to be on a different track than you are, and you might enjoy. or at least be interested, in the discussion underway.> From Ion, <Everything is ruled by mathematics, as all wise humans know by now. Didn’t wise Plato put this inscription at the frontispiece of his Academy? ”Let no one enter here who is ignorant of mathematics.”> I am in no doubt that he is on a different track to me. However, we are travelling in the same direction. From Ion, <Of course, there is no 100% certainty in lottery, either. But the main thing is to play smaller amounts of combinations at the most favorable moments. Yes, there are such favorable moments that lead to a profit.> I agree entirely. There have been many favourable moments. However, as far as I know, no one on this planet has ben able to predict them. I didn't find any accounts on Ion's site detailing his winnings in the last twelve months, for example. Added: Here's an idea for you to think about: Retrospective prediction. The UK lottery has had 945 drawings so far. Take the first 800, for example, and apply any historical method to predict the 801 drawing. Now move the base from '1 to 800' to '2 to 801' to predict the 802 drawing and so on. We can do this 145 times before we run out of data. Now analyse the results. ------------------ David Roberts [This message has been edited by David Roberts (edited January 16, 2005).] IP: Logged
Donald Darden Member	posted January 17, 2005 07:38 PM Yeah, I tried that years ago. I also allowed for a sliding window that could be expanded or contracted, and to look from 1 to ten drawings ahead. The results were disappointing. While I could look at the data and come up with a specific case or rule that appeared useful, the program would show that in the general case, there was no clear precursor or pattern. ------------------ Old Navy Chief, Systems Engineer, Systems Analyst, now semi-retired IP: Logged
David Roberts Member	posted January 19, 2005 10:13 AM I'm not surprised. Before this thread drifts into the ether I should mention another use for the Hypergeometric probability function. So far, we have used N=population size n=sample size k=number of items in population labelled "success" h(x; N, n, k) = ( kCx * (N - k)C(n - x) )/NCn ... [1] where x = 0, 1, ... , k. with, for example, N=53, k=6 and n=16 (ie the pool size) Going in the opposite direction we can use k as a pool and sk as a subset of k to denote an interest in the behaviour of singletons, doubles, triplets and so on. We now have h(x; N, k, sk) = ( skCx * (N - sk)C(k - x) )/NCk ... [2] where x = 0, 1, ... , sk. For N=49 (as in UK), k=6 and sk=1, for example, we get h(0)=0.87755102 h(1)=0.12244897 (ie 1 - h(0)) So, the probabilty of a number from N not appearing in k is h(0). For it not to appear in two consecutive weeks is 0.87755102^2. For j weeks we have 0.87755102^j. We can ask, how many weeks will a number need to be not selected for that probabilty to be <= 0.05. ie 0.87755102^j = 0.05 giving j = 22.93. So, the chance of no selection for 23 weeks is < 0.05. This morning, 19 Jan, for the UK lottery, 34 has not shown itself for 28 weeks 34[28] and 21 has been absent for 23 weeks 21[23]. The next four are 3[22], 2[20], 13[18] and 14[17]. Now, one school of thought would argue that 34 is a 'hot' number on the basis that if non-bias rules then 34 will have to 'come back'. However, this throws away some information, namely that 34 is currently suggesting bias. Note that I refer to # 34 and not ball 34. We know, only after the event, which sets of balls are used so we cannot consider a particualar ball. We don't need to, # 34 is not behaving as expected. I would argue for excluding both 34 and 21 and, perhaps, 3 ie treat them as 'cold' numbers. Excluding all three reduces my selecting from 49 to 46. 49C6 = 13983816 46C6 = 9366819 No great shakes but better than a poke in the eye with a sharp stick. It should be remembered that the excluded numbers are not prohibited numbers so they may appear in the next draw but this does not contradict our argument. On the contrary, 5 weeks ago 34 had been absent for 23 weeks so its exclusion would have been correct to date. The point of this approach is that it is a suggested better tack than 'assuming non-bias then...' because if non-bias then prediction is pointless and we should simply generate a random selection. On the other hand if a hint of bias at this point in time then, IMO, back it. If the argument is false then we break even. If we end up reducing our chances then this proves bias but we chose the wrong direction. My two cents is on exclusion. In [2] above we can use sk = 1 to 6. Added: One web site has <Most 'overdue' numbers> = 34, 32, 21, 3, 2, 13 even though last Saturday saw 32 being drawn. I agree with them if I go back to last Friday so, it would appear, they haven't updated their calculations yet. The moral here is to use your own data and your own apps. No change there then. ------------------ David Roberts [This message has been edited by David Roberts (edited January 19, 2005).] IP: Logged
David Roberts Member	posted January 19, 2005 02:13 PM <My two cents is on exclusion.> Just lost two cents. I checked out the first (946-800) weeks (except the first 26) of the UK lottery. The first 26 was skipped so as to be more than 22, our criteria. On 1953 occasions a number was found to be 'overdue' by more than 22 weeks. On 236 occasions one such number occurred the following week. Looks good? Nope. By the same token, on 1953 - 236 occasions one such number didn't occur the following week. ie a probabilty of (1953 - 236)/1953 = 0.8792 We have already found that the probabilty of any number not appearing is 0.87755102. I then used, instead of 800, 100 to 700 and got, 0.8704, 0.8742, 0.8767, 0.8845, 0.8797, 0.8745, 0.8776 Another idea bites the dust. ------------------- BTW, I've done a chi-squared test on the UK lottery. A test giving < 5% would suggest an unusual behaviour. 10% is inconclusive but worthy of keeping an eye on. I got between 50% and 75%. At that level the chi-squared tables don't bother with precision as there is absolutely no evidence of anything unusual. However, chi-squared belongs to the L~2-space group of algorithms including the least squares method of curve fitting which tend to give little credence to 'rogue' values unlike algorithms which reside in L~infinity-space. This is why I considered the 'long runs of non-appearance' approach. -------------------- My first post in this thread said. <Lotteries are determinate systems and as such the theoretical odds against winning whatever strategy is used is the same for each and every one.> I should read my own press. ------------------ David Roberts [This message has been edited by David Roberts (edited January 19, 2005).] IP: Logged
Donald Darden Member	posted January 20, 2005 02:36 AM That's deep, Dave. Real deep. I'm going to have to struggle through that a few times. But I think the arguement got down to the discussion of whether there was ever a favorable moment when a certain strategy might beat the odds. We agree that by hindsight, such moments do seem to appear. We also agree that over the course of the lottery, those moments are lost in the "normalization" of the lottery. No pattern can persist without showing evidence of an underlying bias. So I think the focus is now on two remaining issues: (1) What determines that we are on the advent side of such an occasion, and (2) what strategy does that apparent opportunity tend to support? In other words, instead of sliding off again towards the long view, we are trying to look at the lottery in some sort of myopic manner that resembles the moment of decision when we would try to decide what to play. It may seem rediculous, but it's key to whether there are any prospects there at all. Is there something we should be looking at that might give us a bit of an edge? I don't really believe in this, you understand, but it basis for trying to run the numbers again from a variety of perspectives. ------------------ Old Navy Chief, Systems Engineer, Systems Analyst, now semi-retired IP: Logged
David Roberts Member	posted January 20, 2005 06:58 AM (1) What determines that we are on the advent side of such an occasion? (2) What strategy does that apparent opportunity tend to support? I reckon that the answer to (2) will be obvious when we have the answer to (1). With any population there is a minimum sample size below which any conclusions will be suspect. Any conclusions drawn with the minimum sample size are unlikely to change with greater sample sizes. With a lottery we can determine a minimum sample size given required confidence limits. However, our conclusions are likely to be that nothing unusual is going on. If any unusual behaviour exists then it will be short lived otherwise we'd have a different conclusion. So, we should restrict our analyses to sample sizes below the accepted minimum for making general conclusions. I'd already determined that your last 60 months of drawings was less than this minimum sample size. So, you are already employing a myopic stance. Of course, getting suspect conclusions is exactly what we want and we want them to persist for at least one drawing. Every time that I thought I'd found something suspect by examining a particular condition I found that the odds did not differ when that condition was removed. [1] By 'Every time' I mean when I last looked at lotteries at the end of '99. Take my 'long runs of non-appearance' approach. The chance of a 'long runner' not being selected turned out to be no different than the chance of any number not being selected. I excluded the three found above and # 34 was selected. I tried a lot of ideas with my old Atari but some I couldn't try because of a lack of memory and lack of CPU crunch. In fact, some of the things I've done in the last few days I'd have run on the Atari, gone to bed and examined the results after breakfast. With multi-tasking and the GUI the perceived advance isn't that great. On pure number crunching, our machines today are staggeringly fast in comparison. Anyway, as you infer the 'Holy Grail' is to find an approach where [1] is false. I doubt intuition will help and it will probably be a process of elimination. That is, keep trying different conditions until one looks promising. Bit like gambling really. Looking for that one bet which will recoup every thing we've lost so far. Hmmm. ------------------ David Roberts [This message has been edited by David Roberts (edited January 20, 2005).] IP: Logged

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