"The Lysenko Maze", a short story by Donald A. Wollheim (alias "David Grinnell"), originally published in Punch, 30 December 1953. You might have read it in the 1987 Asimov–Greenberg anthology The Great SF Stories #16 (1954). The extracts below are quoted from The Magazine of Fantasy and Science Fiction, July 1954, available at the Internet Archive.
The former Russian scientist makes a passionate case that, while most of Soviet biology is nonsense, there is some truth to the theories of Lamarck and Lysenko, that acquired traits can be inherited.
The professor waved his hands wildly, a little upset at disturbing his newfound friends. "But of course I am not a Communist — do I have to tell you this again? Do I have to show you what I have gone through? Am I not the same man I was an hour ago, yesterday, last month? A good biologist, a good believer in democracy, in freedom of speech and conscience? Da! I am all that — and yet I tell you again, Lysenko is right!"
They agree to a bet and an experiment to prove or disprove his assertion.
I don't see anything about a monetary stake, but they agree to an experiment:
"If," and Raine weighed his words carefully, "you have seen proof that Lysenko's theories of evolution and the heredity of acquired characteristics do work, would you be willing to conduct an experiment here — under our conditions — to prove it again?"
A giant, constantly shifting maze of tubes, traps and feeding stations is built. Mousy routes to safety and food, once learned, change on a daily or hourly basis.
"At first the mice will become confused, for to obtain water they must come to one place, salt another, meat a third, fruit a fourth, and so on. And within the lifetime of each mouse the will see the regular alternation of these places. They will have to learn to determine the next day's alternation in advance, for there will never be enough food for all. As this goes on, as future generations come into existence, new problems will be added, dangers will be placed in the tubes. These mice will have to force themselves to acquire greater and greater skill at solving problems or die out."
The scientists take careful note of the success rate of their mice. Several mouse generations pass. One day there is some sort of equipment failure, perhaps a fire, that sets free the test subjects.
Now the lights flickered again, there was a crackling sound, sparks leaped through the air, and the tube fell apart at the point! The men leaped to their feet as a horde of little beasts poured through. There was a smell of smoke, and as the two men rushed into the outside darkness, they saw that the farmhouse was ablaze.
The scientists stand outside their wrecked lab and dolefully confer. The Soviet scientist reluctantly agrees that there has been no evidence that Lysenko was right. The current crop of mice is no more evolved, no more intelligent that the original generation.
They stood on a knoll watching the building, its records, and the intricate Lysenko maze burning to ashes. Raine grasped Borisov's arm. "You failed. The Lysenko experiment was a failure. It was that blue mouse, you know. And do you know what that blue mouse was?"
The Russian stared at the fire. "It was certainly intelligent. It certainly had contrived a short-circuit, it managed to get all the mice to unite in breaking out. So it was intelligent, and its intelligence came out of the experiment."
"That mouse," shouted Raine triumphantly, "that mouse was not like the others! It was a mutation, a 'supermouse,' a mutant freak with no relation to its ancestors nor to this foolish experiment!"
"Da, da," said the Russian, shaking his head. "I see your point. It makes sense. Those other mice, I have seen them too often. They hadn't changed, they were just gray mice who spread all over the tube confusing all our clever rotations." He sighed deeply.
"Heredity," said Raine, standing in the darkness watching the house burn, "cannot be changed by acquired characteristics. The only mouse that varied, that was above the norm in any way, was simply a freak of nature, an accident of the chromosomes, a mutant, and, one that, thank heavens, was probably sterile, since we saw no other bluish mice turning up."
Hidden off to the side, two scientist mice take careful notes, happily agreeing that nothing has changed and saying that now they can get rid of their troublesome telepathic mice.
Borisov nodded his head sadly. And sitting on the branches of a bush, in close proximity and a little behind him, three gray mice nodded their heads in agreement. Their prehensile fingers, curled around little bits of sharpened nutshells, carefully noted on scrolls of dried skin what their thought-wave-sensitive brains had just picked up. It was good to know that their opinion of their eccentric blue brother with the dictator complex was verified by the Outside Thinkers. Now they could dispose of his troublesome body in peace and get to work in the real wide world.