Subject: 9x3 vs 7x5

Date: Wed Sep 19 21:34:08 2018
User: JackK2018
Message:
Which of the two do the experts (you guys) think is harder?

Date: Wed Sep 19 22:00:58 2018
User: jamesblackburn-lynch
Message:
I actually haven't lost either one of those yet...but i don't play them often. Still, I think 7x5's are harder just because there are more possibilities to consider. But 6x6 and 10x2 are both way harder than either. My thoughts... James

Date: Thu Sep 20 01:45:24 2018
User: joeygray
Message:
I've played them a bunch. I consider 9x3 to be the easiest of the 12-sums. Of course that could be an ideocentric judgement, based either on the sort of player that I am (like what kind of thinking I'm better at) or perhaps which is more likely to cause my descent into just-screwing-around mode as we were discussing on the other thread. I also consider 10x2 to be way easier than 6x6, and 11x1 to be way easier than 5x7.

Date: Thu Sep 20 08:49:42 2018
User: TNmountainman
Message:
Hmmmm……………..I posted some comments last night but they seem to have disappeared...…….

Date: Thu Sep 20 08:59:29 2018
User: jamesblackburn-lynch
Message:
Joey, I definitely enjoy 11x1's more than 5x7 (and 12x0 way way more than 4x8) but one way in which 11x1's are "easier" is that it's easy to tell when they are unwinnable. I don't know how I could ever be certain a 5x7 is unwinnable (even the computer solvers warn they might not be correct when they say one is). It's all those damn possibilities that make them "hard." In other words, I find pressing "Give Up" much easier with 11x1's. Does that count for making them easier? James

Date: Thu Sep 20 09:31:50 2018
User: TNmountainman
Message:
OK...……..….going to try and re-create my comments, which is vexing, 'cause I spent some time composing them...… First of all, 7x5s are definitely harder than 9x3s. I think that's almost "settled law" from earlier discussions on this board. As evidence, there are quite a few more folks knocking off 9x3s at a greater than 99% rate, vs. the several who are for 7x5. Further...……..while all climate 5 games have been won for both variants, there are only 10 or so climate 5 9x3s that have been won only once, as opposed to 2x or 3x that number for 7x5. One could argue that the 9x3s have been played more, but a cursory examination shows that not to be obvious at all. Further still...…………...the 100th least-won climate 5 7x5 has been won only 15.4% of the time, while the 100th least-won game for 9x3 has been knocked off at 26.3%. That same trend is seen through the lowest-won 200 games of each variant as well - and so on. I also believe jamesblackburn-lynch's theory holds some weight, as almost counterintuitively, more possible pathways lead to more dead ends. However, I believe the single biggest contributing factor is how much more difficult it is to clear a column (a huge predictor of success) in 7x5 vs. 9x3. I don't distinctly remember, but surely that factor was presented in earlier discussions. (Which is also what makes 7x5s harder than 8x4s, for example.)

Date: Thu Sep 20 09:55:41 2018
User: TNmountainman
Message:
To extend those thoughts (since you all have since my earlier comments disappeared), that factor (relative difficulty in clearing a column) at some point loses out to fewer free cells available when one drops to 10x2 and 11x1 (and most obviously on 12x0). The hotel had a nice discussion or two or three on that back in the day. So although the 'average' 11x1 may(??) be easier than the 'average' 10x2, there will be more un-won games (there are no un-won climate 5 10x2s) because of that factor in and of itself. Also, the longest streak in 11x1 is 'only' 486, while in 10x2 it is 2693, certainly due in large part to the 30-40 un-won games for the 11x1 category. I believe the hotel had some interesting statistical constructs on all that. james is also correct that 6x6s are harder than 7x5s, again due to the harder-to-clear-a-column factor. Only 3 players have a >99% win rate (with 100+ plays) in 6x6, and the winning percentage of the *300th* least-won 6x6 is only 10% (vs. 23% for 7x5). I believe that someone may even have tried (and failed?) to create some sort of algorithm for difficulty based on free cells and columns. Not positive on that, but I think so.

Date: Thu Sep 20 20:25:57 2018
User: JackK2018
Message:
Nice analysis guys. So More columns is easier than more free cells. That would make sense, I hate the 4x8 games. Even 4x10 is tough. And it seems like a little lucky when I (rarely) solve it.12 x0 is challenging and (almost)fun. And I would like to think that I am pretty good at 13x0.

Date: Thu Sep 20 23:04:31 2018
User: TNmountainman
Message:
More columns is easier than more free cells *only* 'til one gets down to 3 free cells (if we're talking about 12-sum games, as per your original query). And IMO 12x0 is way more fun than 13x0. In 13x0, most are either too easy, or you run into one of the unwinnable ones. Which is really why the winnable subsets were 'invented'. Altho the variant that drove that move was more the 12x1, as I recall without going back to check, due to the very few unwinnables therein. Players would run up huge streaks, only to be thwarted when stumbling upon one of those, and then grumble about it.