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I read the story for the first time in 1982 or 1983, so obviously it is written before that period. The plot, at least what I remember is following:

There are two hostile space craft fleets facing each other. It could be that the one is from planet Earth. The space ships do not shoot at each other. However each of them has a computer that calculates their chances to win. The one fleet (maybe the one from Earth) has, according to the computer, no chance to win and the soldiers are lethargic and demotivated. Then a consultant is sent to that fleet. He monitors the situation for some time and then advises the soldiers to shoot at their own discretion. After a while they win the battle.

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    Hi, welcome to SF&F! Do you remember if this is a book or a short story? Any idea what the cover looked like?
    – DavidW
    Commented Feb 19, 2021 at 15:01
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    That said, the idea that a lone human from Earth saves the day against an enemy the computers determine can't be defeated is the plot of Hour of the Horde, which you can read about here: scifi.stackexchange.com/a/203452/101407
    – DavidW
    Commented Feb 19, 2021 at 15:03
  • Also a variant on this very early in the Buck Rogers series.
    – Separatrix
    Commented Feb 19, 2021 at 16:30
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    Also the Doctor Who story Destiny of the Daleks. en.wikipedia.org/wiki/Destiny_of_the_Daleks I have to wonder if Terry Nation ever read Fool's Mate.
    – Pete
    Commented Feb 20, 2021 at 0:20

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This is almost certainly "Fool's Mate" by Robert Sheckley.

The fleets are commanded by computers that are so advanced that they can predict exactly each other's strategy, and therefore will never attack unless they have an advantage. Neither has a clear advantage in attack, but both have an advantage if they stay on defense; and so they stay. Everyone on board the Earth fleet knows that in about two years' time the odds will be so good for the adversary that they will attack, and win. Unless they make some deployment error and get massacred even earlier.

Ellsner, a consultant from Earth, gets this explanation from General Branch and refuses to accept it. Meanwhile the men slowly go crazy under the tension.

In the end,

Ellsner recruits Nielson, a pilot who cracked under the stress, to pilot the whole fleet. He's totally bonkers, so his strategy is crazy and suicidal -- the enemy computer pauses to analyze the strategy, because its programming says there is always a strategy - and finds nothing. According to the programming, the computer impassively waits for a rational pattern to emerge, while its ships are wiped from the board.

The story can be read on the Internet Archive(in this edition the Omar Khayyam quote seems to have gotten messed up).

A similar concept (a CPC having problems dealing with human realities) is present in Mack Reynold's 1967 "The Computer War". Something vaguely akin to this briefly appears in John Wyndham's The Outward Urge, with killer robots attacking a base on the Moon.

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    "We are getting wiped out. Why isn't the computer DOING anything." "Sir, I may have a solution. There is an old program in the library called AlphaGoZero. Apparently it was written by a M. Guh. Guh Gel. I can patch it in if you want." "At this point it can't get any worse. Set main computer computer to slave mode, priority override to the archival program." ... "Sir I detect tactical advantages on all skirmishes. I think it's working!"
    – David Tonhofer
    Commented Feb 19, 2021 at 19:17
  • @user14111 thank you! I was not able to quickly find it on the Archive, and only found it on Google. I have edited the answer.
    – LSerni
    Commented Feb 20, 2021 at 0:02
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    @va-0907: This plot idea is amusing, but is really nothing more than a fool's tale, as would be obvious to any reader who actually knows any bit of game theory...
    – user21820
    Commented Feb 20, 2021 at 13:28
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    @user21820: Sorry, my mistake. I did not know that this is actually a forum for math and game theory. I thought this was a sf forum :-) ;-) :-)
    – va-0907
    Commented Feb 21, 2021 at 6:19
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    @va-0907: Nah not anyone's mistake; I was just commenting. Many science-fiction stories are based on incorrect understanding of science, so we have to just read them for the laughs. I was just putting my comment out there for people who didn't actually realize that the 'science' was wrong. It is hard for untrained people to tell when the story tries/pretends to be hard science-fiction but fails. =)
    – user21820
    Commented Feb 21, 2021 at 7:44

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