Subject: Grr...
Date: Tue Nov 12 12:09:53 2019
User: joeygray
Message:Two impossible 13x0 in the same morning. Grrr... Almost makes me want to cross over to the Dark... I mean, ix's side.
Date: Tue Nov 12 12:15:34 2019
User: TNmountainman
Message:Staaaay in the light.....
Date: Tue Nov 12 12:20:05 2019
User: TitanicTonys_deckofcards
Message:Well, there *is* another way, you know...................................................sorta.................
Date: Tue Nov 12 17:06:43 2019
User: Oded789
Message:If by crossing to the dark side you mean switching from regular 13x0 to w13x0, I'll share that my previous modest three streaks of 13, 19 and 6 were snapped each time by an unwinnable, prior to my current 32 and counting. Let's see how long before my luck runs out again. I was also contemplating moving to the dark side...
According to free@last stats, assuming you win every winnable game, there's only a 23.5% chance of making a 50 streak, and less than 2% of making it to 100. The odds for the all-time record of 197 are 0.01%.
Date: Tue Nov 12 20:04:10 2019
User: joeygray
Message:Four obviously unwinnables today. Grrr.
But Oded, are you sure that’s right? I have an all time high of 81 and I’m only in 500th place. If it was that improbable I would’ve thought there’d be fewer who did it.
Date: Tue Nov 12 20:24:59 2019
User: Oded789
Message:Yeah, I'm pretty sure.
There are 1654 (out of 32768) unwinnables on level 10, meaning 94.95% win rate.
Meaning if you already got to 50 (I'll spare you that math), there's a 7.5% chance (0.9495^50) of going from there to 100.
I'm sure free's numbers are correct.
237 players (which surely is less than 237 people :-< but I digress) have streaks of 100 or higher.
Obviously if you play 10000 games the odds are higher that you'll hit a purple patch at some point.
How much higher? Been too long since I've dealt with calculating stuff like that.
Date: Tue Nov 12 22:00:58 2019
User: jamesblackburn-lynch
Message:Wait til Hop reads this. He has a function that calculates the expected winning streak.
I agree with Oded’s math but free’s data isn’t flawless. free always reminds us of that. For example, look at 9x3 level 10’s. According to free’s solver, I think, 10 or so are unwinnable. But in fact, probably only 2 are. Sometimes the solver gave up on a winnable game.
James
Date: Tue Nov 12 22:38:07 2019
User: free@last
Message:At 1.5M 13x0-10 games played, unlikely there are many, if any, unwon winnables left.
Date: Wed Nov 13 00:39:17 2019
User: joeygray
Message:I was also going to say that for 13x0, or any zero cell variant, the solver most likely will not run out of tree space and miss a winnable game.
Date: Wed Nov 13 05:09:50 2019
User: HopDiriDiriDattiriDittiriDom
Message:James,
It was posted before (see the link).
The more you play a variant the closer you get to the average streak length provided that you do not lose any winnable.
As for 13x0, I myself have not lost any winnable yet. So I'm getting closer to it...
Link: 13x0
Date: Wed Nov 13 05:35:14 2019
User: Oded789
Message:But Hop, as you say the average streak of 13x0 is only 34.4.
What are the odds of getting at least once to 100 if you play 5000 games? or 10000 games?
Date: Wed Nov 13 06:09:11 2019
User: HopDiriDiriDattiriDittiriDom
Message:But that's based on free's data. Playing 10000 games without losing any winnable games would give you a very approximate result (IMHO).
It could actually be higher than 34.4 if there are some winnable games not solved by the solver program.
Date: Wed Nov 13 17:07:44 2019
User: Oded789
Message:But I'm less interested in knowing what would be your average streak (and I trust your calculations).
The question is what would be your highest, and what's the probability of it being 100 or more given a certain number of games.
Date: Wed Nov 13 18:08:44 2019
User: jamesblackburn-lynch
Message:Oded,
I’m thinking along these lines...
Let’s consider 1000 plays just as an example. We could win the first 100 (and then anything for the next 900) or we could lose the first game, win the next 100 and then whatever for the next 899, or we could win the first one, lose the next one, win the next 100, etc.
We could think of it as winning 100 games in a row out of a 1000 and then move that around, I.e. won the first 100 or games 2-101 or games 3-102. It sounds like some kind of permutation/combination of 1000 choose 100.
But that’s not done because if we did 1000 choose 100 times the probability of winning 100 in a row...or wait...is that enough?
Gotta think more...I always have to create probability from scratch.
James
Date: Wed Nov 13 20:43:00 2019
User: redberet
Message:Me, calicokid and justlucky all hit unwinnables at 40 for todays daily streak, what are the odds on that. I've experience two unwinnables within three games. Didn't mind the second one, I like my unwinnables at the beginning of a streak.
Date: Thu Nov 14 19:21:26 2019
User: jamesblackburn-lynch
Message:Okay, I’ve thought more about Oded’s question.
I went and found a relevant discussion on math.stackexchange. Link below if you wish.
This turned out to be a well-known difficult problem. For us the question is: what is the probability of winning k games in a row in N attempts given that we know the probability of getting a winnable game (and assuming we always win those).
I tried k=100 and N=1000 with Oded’s probability of .9495 chance to get a winnable in 13x0.
I had to slightly modify the recursion in the link. But basically we calculate the probability of winning 100 in a row in 100 tries (easy) then use that to get the probability of winning 100 in a row in 101 tries.
The basic idea of the formula is, for example, if you want the probability of winning 100 in a row in 201 tries, first get the probability of winning 100 in a row in 200 tries. Then...how else could you win 100 in a row with the one extra game? The only way is to not win 100 in a row in the first 100 tries, then lose a game (your 101st game) and then win games 102-201. That way you win 100 in a row and this way cannot be counted in the ways you won 100 in a row in the first 200 games. You needed that 201st. Because the events are mutually exclusive we just add the probabilities.
I used 201 as an example because that’s the first time this method works. I had to fix it before we played 201 games but it wasn’t hard because if we play less than 201 games, say 200 games, then there is no way to win 100 in a row in the 99 first games. So that part of the formula is just 0.
Now having said all that, I put this in Excel and either the whole thing is wrong, or the error term for Excel when calculating all these numbers is getting too big, because eventually I get the probability is larger than 1. Obviously, that can’t be right.
Because I am adding such small numbers and Excel has to round, it is possible that the formula is correct and Excel is the problem.
My results say after 200 games you have a 53% probability of having a streak of 100 or more. That seems crazy high to me. But by the 300th game it has only increased to 56% chance. The numbers we are now adding are much smaller than even the small numbers we were adding at the beginning (i.e. .9495^100), so the probability is very slowly rising. It should asymptotically approach 1.
It isn’t until we reach the 624th game that now the probability is 60%. Then it rises very quickly. That shouldn’t be but one round off error here will loop back on itself quickly.
I am still suspicious about how fast it goes to 50%.
But that’s my first try.
James
Link: https://math.stackexchange.com/questions/234062/probability-of-tossing-a-fair-coin-with-at-least-k-consecutive-heads
Date: Thu Nov 14 19:34:44 2019
User: jamesblackburn-lynch
Message:Ooops! Found my error at the beginning. I forgot to correct their situation for ours (flipping a fair coin where winning and losing are equal probability).
When I fixed my error, the probabilities went WAY down.
To win 100 in a row in 200 tries: 0.061515927
To win 100 in a row in 500 tries: 0.115030683
At 626 tries, Excel loses its mind. I need to do this in Maple.
James
Date: Thu Nov 14 23:43:35 2019
User: HopDiriDiriDattiriDittiriDom
Message:James,
We had discussed it (check the link) here and come up with the formula. You don't remember?
I copy my PARI/GP function for it here:
pf(n,v)=
{
my(s=5+if(n<50,n,50)10,d=2.^15);
prod(i=5,s-1,
(1-v[i-4]/d)^10)*(1-v[s-4]/d)^(n-if(n<50,(s-5)*10,50)
)
}
For example it would be like this for Oded's question (what's the probability of it being 100):
? pf(100,[521,690,888,1137,1408,1654])
%3 = 0.01777615253896395935906896633
And for it being 200:
? pf(200,[521,690,888,1137,1408,1654])
%6 = 0.0001000988319884603943182845826
Link: streak probability
Date: Thu Nov 14 23:59:39 2019
User: jamesblackburn-lynch
Message:Hop,
As I said in that thread, I can’t read your code. I don’t know what it does. But I thought when we were talking about it before we were talking about the probability of winning 100 in a row in a given variant. I did not realize your code was figuring out the probability of winning 100 in a row for a given number of games like we are talking about here. I wasn’t doing that before, at least.
I can’t really understand your code because it references so many things I do not know...e.g. what is d? What is the function my()?
But it looks like you are just multiplying the probability of winning the first ten then the next ten and so on, until you get to fifty and then you are level 10 and it doesn’t change anymore.
But that’s just the probability of winning 100 in a row. His question allows you to not win 100 in a row a bunch of times but still win 100 in a row after playing a lot more than 100. That is, you play 1000 times...now what is the probability somewhere in there you win 100 in a row? That’s a different question from what I believe we discussed before.
James
Date: Fri Nov 15 00:32:13 2019
User: HopDiriDiriDattiriDittiriDom
Message:OK,
Forget about my() it's just a PARI/GP pecularity.
Yes as you say it just multiplies the probability of winning the first ten then the next ten and so on, until you get to fifty and then you are level 10 and it doesn’t change anymore.
Yes my code only calculates the probability of a certain streak length (100, 200) but maybe adjusted for other types questions.
For example
? 1/pf(100,[521,690,888,1137,1408,1654])
%7 = 56.25514282733999391245683859
if you play to build a 13x0 56.26 times you can make a streak of 100 (at least once).
Average streak length is 35.39305858931120775814001857 so
? 1/pf(100,[521,690,888,1137,1408,1654])*35.39305858931120775814001857
%8 = 1991.041566038114552449631251
that means if you play 1991 games without losing any winnable games you can have a streak of 100 (at least once).
Date: Fri Nov 15 00:52:07 2019
User: joeygray
Message:So I should feel pretty good (or pretty lucky, I guess) that I got an 81 streak in my first 500 games? I haven't been past 35 since.
Date: Fri Nov 15 01:16:57 2019
User: HopDiriDiriDattiriDittiriDom
Message:Yes you seem to be lucky.
? 1/pf(81,[521,690,888,1137,1408,1654])*35.39305858931120775814001857
%9 = 744.2051354509447621936707845
Maybe we should say "you need to play 744 games at worst to make a streak of 81".
Date: Fri Nov 15 08:50:16 2019
User: jamesblackburn-lynch
Message:Hop,
I don’t get it. Of course one could not win 81 in a row even after 744 games. What do we get by dividing the average streak length by the probability of winning 81 in a row?
Joey, not crazy lucky but, yeah, lucky.
James
Date: Fri Nov 15 09:40:27 2019
User: HopDiriDiriDattiriDittiriDom
Message:James,
You know nothing is certain in probability. Maybe it can be better stated as
"You need to play 744 games at worst to make a streak of 81 with 99% certainty."
Of course I'm not sure about "99% certainty". It could be "98% or 99.5%. But should be something close to 100%.
Date: Fri Nov 15 10:14:23 2019
User: HopDiriDiriDattiriDittiriDom
Message:James,
Sorry I missed this bit: "What do we get by dividing the average streak length by the probability of winning 81 in a row? "
I'm not dividing but multiplying with average streak length. You seem to misread.
Date: Fri Nov 15 10:39:35 2019
User: jamesblackburn-lynch
Message:Right. You are dividing the average streak length by the probability. I did say it correctly. Sorry I wrote it in a complicated form
I believe what you are finding is the "Expected" number of games one would need to get a streak of 100. The expected value being sum (x*P(x)) where x is what you want and P(x) is the probability it occurs. So by dividing by the probability you are (sort of) getting the original x back.
Perhaps that is what Oded wants but his original question is about the probability of winning 100 games out of 1000 plays (or 10000) or so on. That is not the same.
I'd say there isn't no confidence interval for your answer. That is we can't be 99% sure it is correct or 85% even. That would depend on the distribution of the numbers.
free, that is it! I just finished doing the calculations in Maple. I got the probability of winning 100 in a row out of 1000 for a success probability of .9495 is .2353416123
The calculator you just show me gives 23.53%.
That means mine works!! I'm happy because I just saw your message when I finished mine. Of course, had you sent that before I wouldn't have had to come up with it myself. In other words, thanks for not showing me that until it was too late.
James
Date: Fri Nov 15 11:29:46 2019
User: free@last
Message:"Of course, had you sent that before I wouldn't have had to come up with it myself. In other words, thanks for not showing me that until it was too late."
You are welcome! :D
Date: Fri Nov 15 12:10:30 2019
User: jamesblackburn-lynch
Message:So Oded can use free's link to answer any of his questions, but having my own, I did look at the big one.
What is the probability of winning 197 (the all time streak) after 10000 games? Answer: 1.81%
So that tiropetea did it in 235 games is utterly, stunningly lucky.
James
Date: Fri Nov 15 13:52:46 2019
User: HopDiriDiriDattiriDittiriDom
Message:So James,
Can your 12x0 record be considered lucky? 67 resisted for a long time but you broke it playing not so many number of games.
Date: Fri Nov 15 13:55:59 2019
User: TNmountainman
Message:..........except, james, he (supposedly) did it in 198 games (see bottom item below).
tiorapetea has had some interesting things discussed in the past. I offer for your all's perusal. VERY especially see last item:
https://www.freecell.net/f/c/disctopic.html?code=657&replies=5
See Laffman's penultimate post on that page. And the last post on that page is a link to the hotel. I don't have time to try and find that on the wayback machine, but maybe roo or someone else can search that out.
-----------
https://www.freecell.net/f/c/disctopic.html?code=11581&replies=56
On page 2, see my post on Jul 6, and then huffy's followup on Jul 7.
-----------
https://www.freecell.net/f/c/disctopic.html?code=6423&replies=15
See ElGuapo's comments in the penultimate post.
--------
https://www.freecell.net/f/c/disctopic.html?code=9985&replies=6
tiorapetea actually makes some comments in 2011.
--------
https://www.freecell.net/f/c/disctopic.html?code=1476&replies=15
VERY interesting discussion. Did you all know tiorapetea's 197-win streak happened in the first 198 games played?!?!?!?!?! I'll let you all calculate THOSE odds!
Date: Fri Nov 15 14:25:17 2019
User: HopDiriDiriDattiriDittiriDom
Message:huffy's followup: "that tiorapatea was somehow doing something to get dealt winnable games."
How can it be possible? The dealer runs on the server. So he hacked the server back then?
Date: Fri Nov 15 14:39:57 2019
User: TNmountainman
Message:I'm not personally making a judgement. I wasn't around back when tiorapetea started all the commotion. But winning 197 out of the first 198 13x0s one plays?? That's quite beyond absurd probabilities, it seems. And we *do* know (supposedly from those wise ones here longer than myself) that the site and or statistics were somehow hacked or corrupted at some point in time, to some degree. I'm just catching some of you newcomers up to speed on some of the history of questionable records.
Date: Fri Nov 15 14:53:55 2019
User: ix
Message:as i remember, it was the first 197 out of the first 197 played, which is quite remarkable. but i think SirPape having a streak of 3 in 4x4 might be even more statistically significant
Date: Fri Nov 15 14:57:28 2019
User: TNmountainman
Message:Yes; and I think you're right on both counts (without doing the math). And both have long been considered extremely suspect.
Date: Fri Nov 15 15:01:59 2019
User: HopDiriDiriDattiriDittiriDom
Message:James after his record breaker 67 made another streak of 40 something (I don't remember the exact number) right after.
67+1+40=108
So losing 1 game out of 108 games in 12x0 vs. losing 1 game out of 198 games in 13x0. Which one is more probable?
I'm just curious.
Date: Fri Nov 15 16:16:33 2019
User: Oded789
Message:Thanks for the link, free.
Hop, that's not a fair way to show these stats. Those weren't James' only 108 games in 12x0.
TN, I've already given the odds of winning your first 197 (or your next 197) above, it's 0.01%.
It's not the same as winning 197 in a row at any point.
According to that streak calculator, you have to play more than 130000 times(!!!) to have a 50% probability of making a 197 streak.
Note that since the win rates are higher for the first 50, the average win prob is not 94.95% but 95.51%.
Apparently 988 games are needed to have a 50% probability of a 100 streak.
Date: Fri Nov 15 22:29:45 2019
User: jamesblackburn-lynch
Message:Ah yes, 67 in a row and then not much later (can’t say it was without a few short streaks in between...like the same day) I got to 40. Those were the good old days.
TN, you really need to write and book and sell it on Amazon to teach us how to use Denny’s crappy search function.
But I don’t get those old claims. Bot or not doesn’t affect getting winnable games. I see the claim that tiorapatea somehow tricked the server into giving only winnables or just hacked the stats directly, but how does it being a bot help?
Too bad no one asked them when they were on the discussion board.
James
Date: Sat Nov 16 03:20:14 2019
User: TNmountainman
Message:Just briefly, those excerpted threads were certainly not exhaustive, but I think a good representation. I felt bad about not providing html links for all those, but that would have meant a lot of separate posts.
I don't quite know how to take tiorapetea's comments in 2011. They seem almost too....uh.....blithe (sorry Denny) and innocent - like full of childish enthusiasm. My vague memory is that, before him, there was a more or less 'proven' example of some sort of hacking, with "Bristol.City.Club" (if I remember the 'spelling' correctly) being the guilt entity. And others strongly suspected. But I believe other commentators here are more capable of addressing those specifics. And no, I don't know how it was done.
And, james, I also thought your next streak of 40+ wasn't immediately after the 67. I've probably had ~10-12 streaks of 40 or more in 12x0, but getting to 60+ from there is "a whole 'nuther thang". But I'll say it again......winning the FIRST 197 games of 13x0 you ever attempt - and nobody has ever topped that, in millions (I think; not gonna look it up) plays, just doesn't pass the smell test, but that's my personal reaction and not a judgement. And earlier today I checked............no other nick for him on that email address - meaning he was not someone who generates a new nick for separate attempts at something.
For comparison(?).......to the relative newcomers..........you all should read SirPape's comments as he was making his big splash - actually doing a Ruthian "called shot" before his third one. He's either got some strong psychic abilities,. ...........or..........or............
Date: Sat Nov 16 10:42:40 2019
User: TNmountainman
Message:Clarification to the above..............it was "Bristol.City.Football.Club".
Date: Sat Nov 16 16:34:02 2019
User: Oded789
Message:TN, I couldn't find anything about BCFC.
What was suspect about his results?
Newcomers won't know you mean 4x4 talking about SirPape.
I don't know how many games he'd played up to then but with his current amount (over 10000 - the most ever), the odds of streak of 3 are 2.94% on paper. However, unlike 13x0, there's no way a human being would win every winnable narrow game. Not even the best player taking a lot of time (which he didn't).
If we calculate by his own winning percentage (0.5% as opposed to the 1.43% winnables rate) then the odds of such a streak are 0.13%.
But almost no-one ever plays that. I wanted to win one and was the first to even try in more than 6 months (and shortly after I managed to do that he won one too). Only three more played it over the last 18 months.
In a different way than 13x0, this too is more luck than skill, but given enough plays, luck should even out. I wonder what would happen if Hop, Kaos or one of the other tough game specialists would concentrate on 4x4 for a few hours, or days.
Link: 4x4 streak - the only one
Date: Sun Nov 17 10:24:36 2019
User: TNmountainman
Message:As I wrote above, Oded, I wasn't around for the Bristol.City.Football.Club sequence(s), and others here, should they be so inclined, are better able to describe that situation.
I believe (from memory only) the link you provided above is the best one to read about that SirPape 'event'. It was discussed elsewhere since, too, but that may be the best accounting. And do I understand correctly that there had been only 3 plays (besides you and SirPape) of 4x4 over 18 months - and that there had been none before your attempts for more than 6 months? That's amazing, as it's mentioned fairly frequently (but mostly in a joking sense).
As roo stated (in referring to his streak of 11 in 10x0): "Such improbable streaks can be achieved against the odds, because statistics works like that, and in a lottery *someone* has to win the big prize!"
So............it may be legitimate. It may not be. I just don't know, but the 'weirdness' of how he did it just raises MUCH suspicion.
Date: Sun Nov 17 17:16:51 2019
User: Oded789
Message:Okay I read those two threads, I don't know if custom mode was different 12-15 years ago and could one choose level 5 and play anything for streak, but I don't see any evidence from BCSC's scores that looks suspicious.
At most he tweaked something to let himself play these variants for streak purposes, without cheating. Not even sure that he needed to do that.
His 6x4 streak of 16 may have seemed unusual at the time, but not anymore.
You took firenze's joke (that he loves 4x0 most) much too seriously...
And yes, that is what I was saying regarding 4x4 recent play, or lack thereof.
You said on that 7x0 thread nearly a decade ago "I guess it surprises me because many on this site are into what some would call the extremes or esoterica of challenges. And many or most have been here longer than I, so I was expecting that all these variants had been tried out an at least cursory levels. When there are movements to try and solve *all* of particular variants, at least at a particular level, there have got to be some extremely, uh, dedicated players here."
Well, I like those esoteric challenges, and now that streaking 8x0 or 7x1 isn't hard via custom mode, set a goal to myself of winning one game each that would count for a streak. The odds for a random deal for both are considerably higher than for 4x4.
I was very surprised to see that I'm the only one to make the lists in either in 7-8 years.
I've actually won two 8x0 games out of 5 (W-L-L-L-W), but forgot to mark the "count for streak" box on the first of those.
Date: Wed Nov 18 21:07:40 2020
User: Oded789
Message:Since this thread is about the odds of improbable streaks, it has just dawned to me that after 12 years, SirPape's mythical 3 isn't the only 4x4 streak anymore.
Zonny currently has a streak of 2 (after winning 5 of his first 872 tries).
Post follow-up