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This is often stated as being the shortest stalemate ever, however, is it actually the shortest?

I am looking for any brute-force attempts that show that 10 moves is the absolute minimum for a stalemate in the game of chess.

Oddthinking
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picakhu
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  • impossible to answer, as you don't qualify the answer as "shortest published stalemate". There could always be something that wasn't published. – jwenting Jun 05 '11 at 04:11
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    @jwenting, it may be possible that someone somewhere has brute-forced it. – picakhu Jun 05 '11 at 04:15
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    Brute-forcing this will be difficult. It would be necessary to brute-force everything up to nine full moves long, which is eighteen plays (nine White and nine Black). Assume a rough average of 20 choices per move (which is true of the start of the game, and usually increases some during play) that's 20^18 possible games, which looks to be roughly 10^23 or 2^78. I don't know if that's actually feasible. – David Thornley Jun 05 '11 at 04:42
  • @David, perhaps there is a non-brute force but still mathematical way of solving it. – picakhu Jun 05 '11 at 04:47
  • also, a quick check with the best computer(1 pflop) and your approximation predicts about 3.16 (approximately pi) years for the computation. Not too bad I say. – picakhu Jun 05 '11 at 04:49
  • @picakhu: Your calculation looks like you're approximating 10^23 floating-point operations, which is far short of the reality. Each of those 10^23 games is composed of 18 choices (with a relatively small handful with fewer), and I doubt you can calculate a particular move with one flop. – David Thornley Jun 05 '11 at 13:33
  • Also, one peta-FLOP = 1000,000 GFLOPS. At $US1.80 per GFLOP (http://en.wikipedia.org/wiki/FLOPS#Cost_of_computing), that's $US1.8m for 3 years. Again, on the false assumption of one FLOP per position. – Oddthinking Jun 05 '11 at 13:58
  • @David, there are going to be a lot of duplicate positions between the different games. I think it is fair to drop the estimate by one or two orders of magnitude... – Oddthinking Jun 05 '11 at 14:02
  • @Oddthinking, we are making a gross assumption here that all these positions/games need to be considered. There MUST exist some way to mathematically distill the number of necessary games. – picakhu Jun 05 '11 at 14:02
  • @picakhu, looks like our last two comments were be written at the same time, with much the same point. – Oddthinking Jun 05 '11 at 14:04
  • @Oddthinking: Certainly, there will be a lot of transpositions. Are we better off doing a strict bounded depth-first search or keeping track of all positions? The DFS just requires lots of processing time, while the positions will also take a whole lot of memory (I don't have a good grasp on how many positions there will be). – David Thornley Jun 05 '11 at 17:16
  • @picakhu maybe, but if they never published it, it's impossible to know about it for others that they did... – jwenting Jun 06 '11 at 03:30
  • @David, seems to me that you do neither. Surely this is the perfect problem to be solved with a Mechanical Turk... http://en.wikipedia.org/wiki/The_Turk http://en.wikipedia.org/wiki/Amazon_Mechanical_Turk – Oddthinking Jun 06 '11 at 03:33
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    How is this on-topic? This belongs on boardgames.SE. – MrHen Jun 06 '11 at 17:24
  • The problem of the dfs isn't just sacrificing computational speed for memory, but you're also risking not finding the most optimal (ie shortest) solution. It would at least have to be an iterative deepening graph search to even guarantee finding the best solution. – Razor Storm Jun 06 '11 at 18:04
  • @Razor Storm, Or do an exhaustive search (i.e. run DFS to completion, perhaps trimming later attempts after they exceed the length of best known one.) – Oddthinking Jun 07 '11 at 12:01
  • What benefit would that have over an iterative technique? On average the iterative technique would only need to run over half the permutations. – Razor Storm Jun 07 '11 at 15:58
  • @Oddthinking: No, this is a perfect case for Korf's iterative deepening search. Search out to, say, four full moves, then four and a half moves, etc. This actually takes little more time than doing the full DFS out to the planned limit, since the number of games searched for each given number of plays is far more than the number searched for with one fewer play. – David Thornley Jun 09 '11 at 12:25
  • @Razor, @David, sorry. Was being pedantic, pointing out another solution did exist, not suggesting it was superior in any way. – Oddthinking Jun 09 '11 at 13:22
  • There is now a [Chess.SE](http://chess.stackexchange.com/) which might be more suitable for similar questions. – Oddthinking Nov 02 '12 at 02:47

1 Answers1

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Yes, it is the shortest stalemate ever found.

It was discovered by Sam Lloyd. [Ref]

Frederick Rhine discovered a similar stalemate, also in 10 moves: 1.d4 c5 2.dxc5 f6 3.Qxd7+ Kf7 4.Qxd8 Bf5 5.Qxb8 h5 6.Qxa8 Rh6 7.Qxb7 a6 8.Qxa6 Bh7 9.h4 Kg6 10.Qe6. [Ref]

Lloyd's contribution continues to be quoted on many sites maintained by experts as the shortest stalemate ever found, despite there being strong competition to beat it.

Note: Some juniors in Sweden actually played out this (pre-arranged) match in 1995. [Ref]

Oddthinking
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    My question was about it being absoluely the shortest. Not if it was the shortest known/found. I.e. have any brute force attacks been made at this puzzle. – picakhu Jun 05 '11 at 02:22
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    it's the shortest ever published. Noone can know if something shorter was ever found or is theoretically possible as such would never have been published :) – jwenting Jun 05 '11 at 04:10
  • @jwenting, "such would never have been published", why is that? – picakhu Jun 05 '11 at 04:27
  • @picakhu, I think @jwenting is being tongue-in-cheek. If someone did a brute-force effort, and found a smaller solution, it is very likely it would have been picked up by the chess-puzzle community. It hasn't been. So, either it has never been performed or it didn't find anything shorter. Either way, I have nothing further I can tell you. – Oddthinking Jun 05 '11 at 10:01
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    Link to Geocities, I am skeptical. – Marco Ceppi Jun 05 '11 at 16:30
  • @Marco - Well played. :) –  Jun 06 '11 at 01:16
  • One example link of many! Even Geocities users are right twice a day! :-) – Oddthinking Jun 06 '11 at 03:30
  • @picakhu if it's not published you can't know about it. If you can know about it it must have been published. Of course there are a lot of published things you also don't know about, and a lot of other things that are published that are blatantly wrong. – jwenting Jun 06 '11 at 03:31