Subject: unwinnables
Date: Thu Nov 29 10:19:34 2012
User: Denny
Message:Recent discussions of the almost unwinnable winnable game 9X2-10 #7669 got me wondering what the actual number of games were that free@last weeded out from the possible games at each difficulty level. Here are the counts of unwinnable games for each winnable flavor, with each row showing the # of unwinnables for difficulty 5, 6, 7, 8, 9, and 10.
8x3: 17 39 68 152 190 253
9x2: 64 105 161 235 368 497
10x1: 557 785 1098 1370 1845 2269
11x1: 32 70 91 139 180 197
12x1: 1 3 3 8 9 16
13x0: 521 690 888 1137 1408 1654
4x10: 228 485 813 1176 1957 2766
5x8: 24 81 146 255 408 544
6x5: 228 535 790 1200 1760 2333
7x4: 27 63 136 238 316 508
That 12x1 looks pretty sweet, huh? I think 13x0 was one of the main motivators for the "winnable" flavor and it's definitely one of the trickiest.
Date: Thu Nov 29 10:28:41 2012
User: TNmountainman
Message:All pretty strong evidence that your algorithm does what it's supposed to.
Please, andyjim, help us out here. Help us find the flaw in Denny's logic.....
Date: Thu Nov 29 11:07:39 2012
User: CubicSprock
Message:wow, this makes some of our winning percentages in the regular variants look pretty bad. I'm shocked that 99.3% of 6x5 and 4x10 level 5's are winnable.
I'm also a little surprised that 9x2 and 7x4 are so similar, with 8x3 having roughly just half the unwinnables...I guess I expected 9x2 to be a little closer to 8x3.
12x1 regular variant certainly is the biggest heartbreaker if you lose a big streak to one of those very rare unwinnable games...makes me kinda glad there isn't a few unwinnables in the 8x4 selection. (i already felt unlucky enough to have my modest 11x1 streak of 92 ended by an unwinnable :P)
Date: Thu Nov 29 13:03:32 2012
User: ginxi
Message:When did you make the game easier? I thought I finslly was getting better at this and am guessing not. I am not a brain but I like the challenge and trying to win.
Date: Thu Nov 29 13:11:33 2012
User: CubicSprock
Message:ginxi,
Denny didn't make the game easier...he didn't change anything. Additional variants were added where impossible games were eliminated, everything in the regular variants stayed the same.
Date: Thu Nov 29 13:56:16 2012
User: joeygray
Message:Oh, I always believed 8x3 was a lot easier than 9x2 and 7x4. I also think 9x3 is noticeably easier than 10x2 and 8x4. Different factors make wides and narrows hard, and in the middle both factors are down.
Date: Thu Nov 29 15:46:53 2012
User: BuzzClik
Message:I note that there are only a few variants listed. The really nasty ones are not addressed -- 4x4, 5x5, etc -- I'm assuming because the majority are unwinnable.
We know that only a couple of 8x4s are not winnable -- what about the rest of the "sum 12s"?
I guess I'm asking about the rationale behind the variants chosen.
Date: Thu Nov 29 16:40:19 2012
User: Denny
Message:Yo, Clik, years ago my deal algorithm had a couple unwinnables in 8x4 but not now.
We picked these variants because they were all close to "streakable" but had some pot holes. But I play a lot of 7x4 and I think there's only been one time an unwinnable took me down. Usually I just lose on a moderately hard one.
The really nasty variants would have so many just plain hard ones they wouldn't likely be very streakable even after we weeded things out.
Now if seems like I need a new variant "Easily Winnable" which weeds out low success rate games too.
Denny
Date: Thu Nov 29 18:53:41 2012
User: Denny
Message:I didn't mean to sound disrespectful by calling you "Clik" Buzz, just feeling silly.
Date: Thu Nov 29 20:50:55 2012
User: ginxi
Message:Cubic Spock Thank you.
Date: Thu Nov 29 21:02:59 2012
User: BuzzClik
Message:Thanks for the explanation, Denny. Makes sense to me.
And, first name, last name, both names. It's all good.
Date: Fri Nov 30 02:24:37 2012
User: TNmountainman
Message:Buzz (or may I also call you "Clik"?), the variants chosen were done by a committee of two - Denny and free@last, back in the Spring of 2011. This board had numerous threads going discussing such, with lots of postings by free@last as he worked through them using Denny's code and his solver.
Below I link just one pertinent thread; there were several, which I'm sure you can find if you're curious enough. Maybe I'll follow this post with one more thread that shows the evolution of those choices.
Link: the quest for unwinnables
Date: Fri Nov 30 03:37:51 2012
User: TitanicTony
Message:My 1st choice for an 11th "Winnable" variant game is 12x0.
My 1st choice for a 12th "Winnable" variant game is 11x0.
And then,
My 1st choice for a new "regular" variant game is 4x11.
This (discussion, site, everything) is fun! ..... THANKS Denny!
Date: Fri Nov 30 05:54:28 2012
User: Goosey_Goosey_Gander
Message:Denny,
How do we calculate the percent winnable from your recent analysis of unwinnables? How many games are there for each variant, and do new games keep getting added? (It seems if I have a good streak going at a level 10 every game is new - 1/1 if I win it).
Date: Fri Nov 30 07:00:37 2012
User: free@last
Message:There are 32768 games for each "difficulty" level.
One reason we didn't do 12x0 winnable was because of how many unwinnables it had; 4000-5000 in level 10 if I remember correctly.
Date: Fri Nov 30 07:34:18 2012
User: TitanicTony
Message:SO WHAT if there are 5000 unwinable level 12x0-10 games??? So far, only 14 players have a streak of >= 50!
YEAH, YEAH, YEAH,... Winnable 12x0!
Date: Fri Nov 30 08:00:53 2012
User: Goosey_Goosey_Gander
Message:32,768 games each difficulty level. That's 2 to the power 16. Something in the construction leads to that I suppose.
Date: Fri Nov 30 08:39:22 2012
User: Goosey_Goosey_Gander
Message:If there are 32,768 games at each level, from the above losing no of games, the losing percentage at level 10 is:
8x3: 0.77
9x2: 1.52
10x1: 6.92
11x1: 0.60
12x1: 0.05
13x0: 5.05
4x10: 8.44
5x8: 1.66
6x5: 7.12
7x4: 1.55
So now it is possible to calculate the chance of overtaking the streak leader based on the number of games behind. Hmmm, I was going to calculate one of the above, but all the ones I play I lead, so lets say I want to play 12X1 from zero and pass javab with a streak of 1,132. 1,133 games at 99.5% 99.5 percent to power 1132 is 57.5%. Chance at lower difficulty levels is greater, but who doesn't blow some winnable games. If I play at a speed of 3.5 mins per game that's 66 hours. 66 hours, no mistakes, 58.5%? Now I know why I don't play 12x1
This is almost more fun than playing.
Date: Fri Nov 30 09:10:05 2012
User: TNmountainman
Message:Tony, I was one who was hoping for a winnable flavor of either 11x0 or 12x0 as that concept was being developed, *if* it (inventing winnables) was going to be done, although since I wasn't doing the work, it would have been a tad unseemly of me to lobby for that. More importantly, I was, and am, happy with the 'regular' flavors, believing that the years of stats have inherent value and thus are more "pure". So, unless somehow by accident, I've kept with the regular games, except for the WWC. I feel the 'separation' of players based on marginal win rates is sufficient for me.
free@last put in TONS of work on this. Any further additional variants would be up to him, most likely. And I do also think that the variants chosen represent a broad and healthy mix of challenges - and of course have led to the WWC, as well.
Although I really didn't think the unwinnables invention was necessary, it seems as though a goodly chunk of people enjoy and prefer them, so I'm glad the efforts seemed to have provided a workable outlet for those players. I think that choice mostly boils down to a preference towards streak length vs. winning percentage. It's always seemed odd to me that Denny set up the main (default) metric that way, instead of winning percentage, like essentially all sporting leagues do. I guess that's me thinking too much *inside* the box, as it were, 'cause I indeed can see the appeal of being able to start fresh again and again, hoping for that "big score".
Date: Fri Nov 30 09:16:02 2012
User: TNmountainman
Message:Oh, and Goosey_, I think you mean 99.95% to the 1133 power (=56.74%, so it's even easier!). And I think surely you can average faster than 3.5 minutes a game on 12x1. (I don't think I've ever played one, but surely....)
Date: Fri Nov 30 10:27:35 2012
User: TitanicTony
Message:TN, not to be picky (more to let you know that I really do read what you write), I'm pretty sure you meant "winnables invention" above (last paragraph, line 1).
I for one prever the "winnable" variants, although I am never going to play W4x10 a lot. My favorite is W12x1 (>5000 games played, 180 hours).
Date: Fri Nov 30 10:43:35 2012
User: TNmountainman
Message:Yes, of course. Thanks...
Also, someone check my math on the above. On my calculator, I get:
.995^1132 = .0034 and....
.9995^1132 = .5677 (and .9995^1133 = .5674, as I stated above)
(And wow - doesn't that show the power of things "at the margin"!)
So I'm not sure where Goosey_ got 57.5%. Maybe he actually did calculate using .9995, and his and my calculators differ that much with that many iterations. But anyway, yes, it's very clear why neither of us is interested in playing 12x1 (no offense!!).
Date: Fri Nov 30 10:57:59 2012
User: ix
Message:>> Although I really didn't think the unwinnables invention was necessary...
tn, think of a player in baseball who has some amazing streak going (i don't know, hits, home runs or something) and a lot of people are pretty excited about it. if you were watching him in a game and the pitcher was pitching around him the whole game, wouldn't you boo?
Date: Fri Nov 30 11:11:16 2012
User: TNmountainman
Message:Hmmm....maybe......maybe even probably. (Actually, in reality, I wouldn't, because I sort of take things as they come along those lines.) But I don't think this is exactly analogous. If one is playing 'regular' freecell, one *knows* there is going to be a situation where the dealer (pitcher) is going to pitch around the batter. Or there's going to be a line drive hit right at a fielder, etc. That's part of the set-up of the game. Ergo, although I certainly appreciate streaks, like Ripken's, Hershiser's, or DiMaggio's, those are a bit more freakish than long-term productivity. Would DiMaggio have gotten into The Hall if his streak had been the *only* highlight of his career?
Obviously, I see your point, but to me, trying to keep my winning percentage at a certain level, or pushing it higher, is more satisfying than winning X in a row of something.
Date: Fri Nov 30 11:14:28 2012
User: CubicSprock
Message:TN, the difference is that the actual number for 32752/32768 is .99951171875 not .9995.
.99951171875^1132 = .57529
.9995^1132 = .56771
like you said...the margins make a difference when raising something to a power that many times.
Date: Fri Nov 30 11:20:07 2012
User: TNmountainman
Message:Got it. Thanks!
Date: Fri Nov 30 11:41:41 2012
User: Goosey_Goosey_Gander
Message:Thank you Cubic... I was about to say that I didn't use the rounded number 99.5%, rather the actual 99.511etc. TN: In the calculations for 12x1 I used the current streak leaders average of 3.23 minutes and rounded it up to 3.5 for no good reason. Now I look and see that I actually played 2,427 games of 12x1 and averaged 2.38 minutes. I had a streak of 601 and after 96 hours of play blew it. Was it a winnable game I lost? Don't know, but going to the bottom after so much effort is why I stick to harder games with a much smaller streak needed to get to the top. That's why I like the winnable variants. I know if I lose a game its my fault, not just bad luck.
Date: Fri Nov 30 12:01:33 2012
User: TNmountainman
Message:Yeah, I understand that. And the way I would look at it (if I wanted to look at 12x1 stats, winnable or not, as a regular thing), you didn't "go to the bottom", you are still in 12th place, all-time (or 8th place, currently):
Link: winnable 12x1, all-time
Date: Fri Nov 30 13:23:05 2012
User: ix
Message:yeah, tn, i know the analogy doesn't bear scrutiny, i just want the opportunity to whiff on something that could have been hit, thats my point
Date: Fri Nov 30 13:37:48 2012
User: Goosey_Goosey_Gander
Message:TNm: What do you look at to say I am in 12th place? or 8th place in 12x1? I only look at current streak and all time. There must be a different way to look at stats that I don't know.
Date: Fri Nov 30 13:45:36 2012
User: TNmountainman
Message:Did you click on the link above, Goosey_? (In fact, you're now in *11th* place.) It takes you to the all-time list, sorted by winning percentage. Maybe you don't know that for any of the streak lists, clicking on "won" at the top of the columns, rearranges the list according to winning percentage. Same can be done for the other headings, too....
I understand, ix. I couldn't hit a major league curveball, either....
Date: Fri Nov 30 13:49:42 2012
User: TitanicTony
Message:GGG, Try sorting by the %won column.
Date: Fri Nov 30 14:27:36 2012
User: Goosey_Goosey_Gander
Message:TNm and TT. Thanks for helping me understand. I did try sorting by win % and came up 11th, now it's back to 12th. But why doesn't it sort strictly by win %? It looks like the number of games played factors in, but how? Can't find anything about that in the instructions.
Date: Fri Nov 30 14:37:30 2012
User: CubicSprock
Message:#wins/(#games+2) is used for sorting purposes
Date: Tue Dec 4 11:51:06 2012
User: Kasenna
Message:Damn it, there are only 16 unwinnables at 12X1, level 10 and I have hit two of them while (by my standards) streaking. The latest is 10799. By all means, join me and 83 others and try it. Now I am off to sulk.
Date: Tue Dec 4 13:16:53 2012
User: CubicSprock
Message:Kasenna,
It obviously isn't fun to lose a long streak to an unwinnable, but that's just the thing with 12x1, there aren't many but when you play enough games you are bound to hit one. Given you've played ~10,000 12x1 games, with a pretty good win rate, I'd estimate you've played at least 6000 at level 10 (and probably more). That is about 1/5th of all level 10 games, meaning you'd expect to have hit about 3 (16*1/5 = 3.2) level-10 unwinnables.
It is not for us to decide whether or not the game handed to us is winnable, all we can decide is to win the game if it is winnable...or we can play the winnables variant, where Denny's power to make us lose via an impossible game is taken away.
Date: Wed Oct 2 21:30:24 2019
User: Oded789
Message:The instructions page and Denny here state that there are no unwinnable 8x4 games on this site, yet two of them have never been solved:
8x4 18461-11 is 0/166
8x4 9216-12 is 0/878
Are those two winnable?
And I'm not quite sure - when you get to level 10 on a streak (50+) can you also get level 11 and 12 games such as these two?
Date: Thu Oct 3 09:55:13 2019
User: TNmountainman
Message:While what you say about the instructions page is accurate, you left out the word "(standard)". This is the sentence:
"It so happens that all our 8x4 (standard) games are currently winnable."
What he means is the games in the 'normal' progression from climate 5 up thru climate 10, which are randomly dealt as one progresses. Climates 11 and 12 are not included in his statement - which is what the "(standard)" caveat means - as they have to be brought up in "custom" mode. These climate 11 and 12 games have been discussed earlier on this board, but I'm not gonna take the time to search out that/those discussion(s). My weak memory is that those are the only unsolvable ones, but don't take that to the bank.
And as to your very last question, one can always (even if you have a streak of 0) bring up those games in custom mode, but *only* in custom mode. In fact, I just called up a random climate 11 game and won it rather easily.
Date: Fri Oct 4 01:38:57 2019
User: joeygray
Message:Actually (to unnecessarily nit you, TN :) ) standard most likely was intended to mean that 8x4 is the standard variant. Standard is the top selection in the variant select dropdown, and when you select it you get 8x4.
You’re exactly right, though (of course) about what is *meant* by that sentence: that all the games you can get by selecting either 8x4 or Standard as your variant are winnable. 1-4 and 11-12 aren’t reachable that way. Aside from custom, you can also possibly get them in tournaments.
Date: Fri Oct 4 01:42:57 2019
User: joeygray
Message:I don’t think anybody knows whether there are unwinnables in 1-4. Tons of them have never been played. Did free ever shoot them through the solver?
Date: Fri Oct 4 02:45:25 2019
User: HopDiriDiriDattiriDittiriDom
Message:Oded,
"And I'm not quite sure - when you get to level 10 on a streak (50+) can you also get level 11 and 12 games such as these two?"
You don't have to make a 50+ streak to get level 11 and 12 games. You can play through custom mode at any level higher than your current level with "count for streak" option.
Date: Fri Oct 4 09:23:41 2019
User: TNmountainman
Message:Yes, joey, that's what I meant (by implication, since 8x4 was what they (both Denny in the instructions and Obed789 in the question) were (already) specifically referring to). But doesn't hurt to qualify even further.
Date: Fri Oct 18 14:59:54 2019
User: Oded789
Message:What are the numbers of unwinnables on each level for 6x6, 7x5, 9x3 and 10x2 ?
Date: Fri Oct 18 15:43:50 2019
User: free@last
Message:Here's all the data I have.
22746 10x0-10.txt
23518 10x0-11.txt
23507 10x0-12.txt
15080 10x0-5.txt
17115 10x0-6.txt
19037 10x0-7.txt
20402 10x0-8.txt
21713 10x0-9.txt
2275 10x1-10.txt
2532 10x1-11.txt
2605 10x1-12.txt
569 10x1-5.txt
794 10x1-6.txt
1106 10x1-7.txt
1373 10x1-8.txt
1852 10x1-9.txt
18 10x2-10.txt
13 10x2-11.txt
16 10x2-12.txt
1 10x2-5.txt
2 10x2-6.txt
5 10x2-7.txt
6 10x2-8.txt
12 10x2-9.txt
0 10x3-10.txt
0 10x3-11.txt
1 10x3-12.txt
0 10x3-5.txt
0 10x3-6.txt
0 10x3-7.txt
0 10x3-8.txt
0 10x3-9.txt
0 10x4-10.txt
0 10x4-11.txt
0 10x4-12.txt
0 10x4-5.txt
0 10x4-6.txt
0 10x4-7.txt
0 10x4-8.txt
0 10x4-9.txt
11930 11x0-10.txt
12414 11x0-11.txt
12673 11x0-12.txt
5925 11x0-5.txt
7212 11x0-6.txt
8652 11x0-7.txt
9647 11x0-8.txt
10992 11x0-9.txt
200 11x1-10.txt
265 11x1-11.txt
297 11x1-12.txt
34 11x1-5.txt
70 11x1-6.txt
93 11x1-7.txt
140 11x1-8.txt
186 11x1-9.txt
0 11x2-10.txt
0 11x2-11.txt
1 11x2-12.txt
0 11x2-5.txt
0 11x2-6.txt
0 11x2-7.txt
0 11x2-8.txt
2 11x2-9.txt
0 11x3-10.txt
0 11x3-11.txt
0 11x3-12.txt
0 11x3-5.txt
0 11x3-6.txt
0 11x3-7.txt
0 11x3-8.txt
0 11x3-9.txt
4769 12x0-10.txt
5188 12x0-11.txt
5147 12x0-12.txt
1841 12x0-5.txt
2387 12x0-6.txt
2973 12x0-7.txt
3470 12x0-8.txt
4201 12x0-9.txt
16 12x1-10.txt
25 12x1-11.txt
18 12x1-12.txt
1 12x1-5.txt
3 12x1-6.txt
3 12x1-7.txt
8 12x1-8.txt
9 12x1-9.txt
0 12x2-10.txt
0 12x2-11.txt
0 12x2-12.txt
0 12x2-5.txt
0 12x2-6.txt
0 12x2-7.txt
0 12x2-8.txt
0 12x2-9.txt
1654 13x0-10.txt
1789 13x0-11.txt
1846 13x0-12.txt
521 13x0-5.txt
690 13x0-6.txt
888 13x0-7.txt
1137 13x0-8.txt
1408 13x0-9.txt
0 13x1-10.txt
0 13x1-11.txt
1 13x1-12.txt
0 13x1-5.txt
0 13x1-6.txt
0 13x1-7.txt
0 13x1-8.txt
0 13x1-9.txt
0 13x2-12.txt
2773 4x10-10.txt
229 4x10-5.txt
485 4x10-6.txt
813 4x10-7.txt
1178 4x10-8.txt
1961 4x10-9.txt
32765 4x4-10.txt
32301 4x4-5.txt
32564 4x4-6.txt
32696 4x4-7.txt
32746 4x4-8.txt
32762 4x4-9.txt
32694 4x5-10.txt
30069 4x5-5.txt
31319 4x5-6.txt
32059 4x5-7.txt
32416 4x5-8.txt
32613 4x5-9.txt
32019 4x6-10.txt
24118 4x6-5.txt
27011 4x6-6.txt
29193 4x6-7.txt
30502 4x6-8.txt
31430 4x6-9.txt
28703 4x7-10.txt
14653 4x7-5.txt
18279 4x7-6.txt
21812 4x7-7.txt
24533 4x7-8.txt
26891 4x7-9.txt
20236 4x8-10.txt
5982 4x8-5.txt
8590 4x8-6.txt
11598 4x8-7.txt
14538 4x8-8.txt
17501 4x8-9.txt
9562 4x9-10.txt
1494 4x9-5.txt
2574 4x9-6.txt
3816 4x9-7.txt
5354 4x9-8.txt
7473 4x9-9.txt
9 5x10-10.txt
0 5x10-5.txt
1 5x10-6.txt
1 5x10-7.txt
5 5x10-8.txt
13 5x10-9.txt
606 5x7-6.txt
544 5x8-10.txt
24 5x8-5.txt
82 5x8-6.txt
146 5x8-7.txt
255 5x8-8.txt
408 5x8-9.txt
55 5x9-10.txt
2 5x9-5.txt
4 5x9-6.txt
12 5x9-7.txt
33 5x9-8.txt
45 5x9-9.txt
0 6x10-10.txt
0 6x10-8.txt
0 6x10-9.txt
32490 6x2-10.txt
29161 6x2-5.txt
30629 6x2-6.txt
31452 6x2-7.txt
32024 6x2-8.txt
32328 6x2-9.txt
27720 6x3-10.txt
15801 6x3-5.txt
19108 6x3-6.txt
22002 6x3-7.txt
24224 6x3-8.txt
26118 6x3-9.txt
13371 6x4-10.txt
3506 6x4-5.txt
5148 6x4-6.txt
7109 6x4-7.txt
9004 6x4-8.txt
11009 6x4-9.txt
2402 6x5-10.txt
3175 6x5-11.txt
3620 6x5-12.txt
269 6x5-5.txt
547 6x5-6.txt
819 6x5-7.txt
1249 6x5-8.txt
1815 6x5-9.txt
174 6x6-10.txt
8 6x6-5.txt
25 6x6-6.txt
41 6x6-7.txt
67 6x6-8.txt
115 6x6-9.txt
19 6x7-10.txt
1 6x7-5.txt
2 6x7-6.txt
5 6x7-7.txt
5 6x7-8.txt
11 6x7-9.txt
1 6x8-10.txt
1 6x8-5.txt
1 6x8-6.txt
1 6x8-7.txt
1 6x8-8.txt
3 6x8-9.txt
0 6x9-10.txt
0 6x9-5.txt
0 6x9-6.txt
0 6x9-7.txt
1 6x9-8.txt
0 6x9-9.txt
32502 7x1-10.txt
32570 7x1-11.txt
32619 7x1-12.txt
29641 7x1-5.txt
30839 7x1-6.txt
31598 7x1-7.txt
32001 7x1-8.txt
32297 7x1-9.txt
24964 7x2-10.txt
26222 7x2-11.txt
26960 7x2-12.txt
13552 7x2-5.txt
16386 7x2-6.txt
19193 7x2-7.txt
21336 7x2-8.txt
23374 7x2-9.txt
7330 7x3-10.txt
8518 7x3-11.txt
9211 7x3-12.txt
1625 7x3-5.txt
2547 7x3-6.txt
3404 7x3-7.txt
4726 7x3-8.txt
5998 7x3-9.txt
532 7x4-10.txt
35 7x4-5.txt
72 7x4-6.txt
145 7x4-7.txt
245 7x4-8.txt
326 7x4-9.txt
30 7x5-10.txt
0 7x5-5.txt
0 7x5-6.txt
1 7x5-7.txt
5 7x5-8.txt
16 7x5-9.txt
0 7x6-10.txt
0 7x6-5.txt
0 7x6-6.txt
0 7x6-7.txt
0 7x6-8.txt
0 7x6-9.txt
26717 8x1-10.txt
27489 8x1-11.txt
27947 8x1-12.txt
16932 8x1-5.txt
19686 8x1-6.txt
22040 8x1-7.txt
23889 8x1-8.txt
25372 8x1-9.txt
6871 8x2-10.txt
7868 8x2-11.txt
8337 8x2-12.txt
1767 8x2-5.txt
2592 8x2-6.txt
3602 8x2-7.txt
4610 8x2-8.txt
5791 8x2-9.txt
273 8x3-10.txt
387 8x3-11.txt
453 8x3-12.txt
23 8x3-5.txt
47 8x3-6.txt
73 8x3-7.txt
163 8x3-8.txt
202 8x3-9.txt
8 8x4-11.txt
1 8x4-12.txt
0 8x5-11.txt
0 8x5-12.txt
30817 9x0-10.txt
31244 9x0-11.txt
31326 9x0-12.txt
26468 9x0-5.txt
28132 9x0-6.txt
29152 9x0-7.txt
29901 9x0-8.txt
30490 9x0-9.txt
11481 9x1-10.txt
12311 9x1-11.txt
12787 9x1-12.txt
4313 9x1-5.txt
5769 9x1-6.txt
7132 9x1-7.txt
8513 9x1-8.txt
10094 9x1-9.txt
519 9x2-10.txt
591 9x2-11.txt
656 9x2-12.txt
70 9x2-5.txt
114 9x2-6.txt
172 9x2-7.txt
239 9x2-8.txt
381 9x2-9.txt
9 9x3-10.txt
14 9x3-11.txt
18 9x3-12.txt
0 9x3-5.txt
2 9x3-6.txt
0 9x3-7.txt
0 9x3-8.txt
5 9x3-9.txt
4 9x4-10.txt
3 9x4-11.txt
1 9x4-12.txt
0 9x4-5.txt
0 9x4-6.txt
0 9x4-7.txt
0 9x4-8.txt
1 9x4-9.txt
2 9x5-10.txt
0 9x5-11.txt
0 9x5-12.txt
0 9x5-9.txt
0 9x6-10.txt
0 9x6-11.txt
0 9x6-12.txt
0 9x6-9.txt
Date: Fri Oct 18 23:57:06 2019
User: Oded789
Message:Thanks a lot, very interesting stuff.
Maybe you missed some of the 5 columns data on copy-pasting?
Here are these numbers converted to winning % (each grid from level 5-10 or 5-12 depending on the data).
Note that in a few cases I've given 3 decimal places.
Grid/Level 5 6 7 8 9 10 11 12
4x4 1.43% 0.62% 0.22% 0.07% 0.02% 0.01%
4x5 8.24% 4.42% 2.16% 1.07% 0.47% 0.23%
4x6 26.40% 17.57% 10.91% 6.92% 4.08% 2.29%
4x7 55.28% 44.22% 33.44% 25.13% 17.94% 12.41%
4x8 81.74% 73.79% 64.61% 55.63% 46.59% 38.24%
4x9 95.44% 92.14% 88.35% 83.66% 77.19% 70.82%
4x10 99.30% 98.52% 97.52% 96.41% 94.02% 91.54%
5x3 no data
5x4 no data
5x5 no data
5x6 no data
5x7 no data
5x8 99.93% 99.75% 99.55% 99.22% 98.75% 98.34%
5x9 99.993% 99.987% 99.96% 99.90% 99.86% 99.83%
5x10 100% 99.997% 99.997% 99.985% 99.96% 99.97%
6x2 11.01% 6.53% 4.02% 2.27% 1.34% 0.85%
6x3 51.78% 41.69% 32.86% 26.07% 20.29% 15.41%
6x4 89.30% 84.29% 78.31% 72.52% 66.40% 59.19%
6x5 99.18% 98.33% 97.50% 96.19% 94.46% 92.67% 90.31% 88.95%
6x6 99.98% 99.92% 99.87% 99.80% 99.65% 99.47%
6x7 99.997% 99.993% 99.985% 99.985% 99.97% 99.94%
6x8 99.997% 99.997% 99.997% 99.997% 99.991% 99.997%
7x1 no data
7x2 58.64% 49.99% 41.43% 34.89% 28.67% 23.82% 19.98% 17.72%
7x3 95.04% 92.23% 89.61% 85.58% 81.70% 77.63% 74.01% 71.89%
7x4 99.89% 99.78% 99.56% 99.25% 99.01% 98.38%
7x5 100% 100% 99.997% 99.985% 99.95% 99.91%
8x0 no data
8x1 48.33% 39.92% 32.74% 27.10% 22.57% 18.47% 16.11% 14.71%
8x2 94.61% 92.09% 89.01% 85.93% 82.33% 79.03% 75.99% 74.56%
8x3 99.93% 99.86% 99.78% 99.50% 99.38% 99.17% 98.82% 98.62%
8x4 100% 100% 100% 100% 100% 100% 99.976% 99.997%
9x0 19.23% 14.15% 11.04% 8.75% 6.95% 5.95% 4.65% 4.40%
9x1 86.84% 82.39% 78.23% 74.02% 69.20% 64.96% 62.43% 60.98%
9x2 99.79% 99.65% 99.48% 99.27% 98.84% 98.42% 98.20% 98.00%
9x3 100% 99.993% 100% 100% 99.985% 99.97% 99.96% 99.95%
10x0 53.98% 47.77% 41.90% 37.74% 33.74% 30.58% 28.23% 28.26%
10x1 98.26% 97.58% 96.62% 95.81% 94.35% 93.06% 92.27% 92.05%
10x2 99.997% 99.993% 99.985% 99.982% 99.96% 99.95% 99.96% 99.95%
11x0 81.92% 77.99% 73.60% 70.56% 66.46% 63.59% 62.12% 61.33%
11x1 99.90% 99.79% 99.72% 99.57% 99.43% 99.39% 99.19% 99.09%
12x0 94.38% 92.71% 90.92% 89.41% 87.18% 85.45% 84.17% 84.29%
12x1 99.997% 99.991% 99.991% 99.976% 99.973% 99.95% 99.92% 99.95%
13x0 98.41% 97.89% 97.29% 96.53% 95.70% 94.95% 94.54% 94.37%
It is interesting to compare these to the actual winning % (link below but also current data).
Perfect play is for computers, especially when it's gets narrow...
Actual Stats 5 6 7 8 9 10 11 12
4x4 0.23% 0.00% 0.00% 0.00% 0.00% 0.78% 0.00% 0.00%
4x5 1.30% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
4x6 4.92% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
4x7 14.00% 9.30% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
4x8 29.44% 35.59% 15.38% 4.17% 30.00% 4.55% 1.82% 1.92%
4x9 37.82% 26.35% 15.47% 15.89% 13.40% 8.91% 9.85% 0.00%
4x10 60.09% 47.62% 34.30% 27.95% 22.65% 19.63% 15.92% 4.00%
5x3 0.79% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
5x4 3.71% 15.91% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
5x5 14.91% 12.50% 100% 0.00% 33.33% 0.00% 0.00% 0.00% (that 100% is 1 of 1...)
5x6 34.94% 60.43% 5.45% 0.00% 11.76% 7.69% 8.33% 10.53%
5x7 52.67% 42.09% 80.65% 70.63% 51.22% 66.67% 10.69% 18.52%
5x8 73.45% 62.83% 52.88% 44.41% 37.87% 33.35% 29.71% 70.00%
5x9 84.62% 89.13% 70.54% 64.47% 59.21% 55.92% 48.93% 53.43%
5x10 90.19% 94.26% 89.35% 85.62% 81.17% 94.04% 75.48% 70.86%
6x2 1.67% 6.25% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
6x3 8.30% 0.00% 0.00% 0.00% 0.00% 3.03% 0.00% 0.00%
6x4 24.69% 16.70% 12.86% 10.56% 8.38% 7.08% 5.75% 3.14%
6x5 55.13% 44.34% 29.83% 25.11% 21.16% 17.78% 15.04% 13.86%
6x6 74.57% 81.79% 54.79% 48.84% 43.18% 38.63% 33.95% 43.84%
6x7 81.87% 90.32% 77.03% 72.52% 67.52% 67.94% 56.90% 60.62%
6x8 91.82% 93.81% 91.07% 88.47% 84.97% 89.93% 76.57% 80.28%
7x1 no data
7x2 13.30% 3.57% 4.76% 5.88% 11.11% 5.26% 3.12% 3.70%
7x3 35.93% 26.58% 18.94% 16.59% 13.94% 11.79% 10.45% 7.67%
7x4 63.85% 74.25% 53.68% 43.05% 36.74% 32.97% 27.41% 32.45%
7x5 83.47% 89.37% 74.05% 67.64% 63.05% 62.37% 53.39% 61.26%
8x0 no data
8x1 11.79% 9.59% 12.50% 4.26% 0.00% 4.55% 0.00% 1.17%
8x2 44.00% 32.59% 22.11% 18.63% 16.64% 14.58% 12.58% 12.52%
8x3 73.08% 79.32% 53.28% 46.24% 41.59% 37.99% 32.69% 21.50%
8x4 85.04% 90.39% 91.05% 90.84% 89.64% 91.26% 62.78% 69.41%
9x0 4.57% 2.27% 1.65% 2.70% 3.66% 1.37% 0.25% 2.17%
9x1 40.65% 24.66% 54.65% 15.38% 18.25% 16.08% 50.00% 25.00%
9x2 76.46% 84.06% 55.46% 49.24% 44.63% 41.39% 35.95% 49.43%
9x3 89.93% 92.62% 84.61% 80.68% 76.71% 77.41% 70.29% 68.82%
10x0 19.41% 9.38% 10.14% 2.74% 4.56% 7.52% 3.65% 17.95%
10x1 69.99% 79.93% 54.68% 46.98% 41.33% 43.15% 33.32% 41.31%
10x2 91.15% 93.62% 87.81% 84.70% 80.44% 86.21% 70.41% 69.53%
11x0 49.51% 33.55% 28.18% 25.90% 24.16% 19.82% 16.82% 19.34%
11x1 90.86% 92.81% 90.25% 88.27% 84.41% 83.96% 66.16% 63.61%
12x0 75.02% 82.46% 58.26% 54.17% 48.99% 46.59% 42.17% 42.54%
12x1 96.82% 97.44% 97.26% 97.05% 96.72% 98.03% 87.38% 85.78%
13x0 88.15% 91.31% 90.82% 89.50% 87.01% 91.76% 68.90% 67.95%
Link: Cumulative Stats
Date: Sat Oct 19 09:28:04 2019
User: free@last
Message:That's all the data. I stopped running things after it was clear Winnables was going to be a small subset and those were covered.
Date: Sat Oct 19 09:57:09 2019
User: Oded789
Message:Can you please run 5x3, 5x4, 5x5, 5x6, 5x7, 7x1 and 8x0 through the solver?
Date: Sat Oct 19 12:05:10 2019
User: free@last
Message:I mean this in the least offensive way possible. No.
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