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It doesn't affect the chance of any one prisoner finding their number - that's still 50%. But the joint strategy massively reduces the independence of the individual prisoners' success, and hence the distribution of the number of successful prisoners.

Rather than a normal distribution (sum of independent outcomes) with a big peak around 50% of the prisoners finding their number and a vanishingly small chance of them all (or none) finding the right number, you end up with a much more complex pattern - there's an approximately uniform distribution in the 0-50 successes range with ~70% of the overall outcome, and a huge peak at the 100 successes point with ~30%.

https://www.r-bloggers.com/2014/08/update-100-prisoners-100-... has a bunch of distribution plots showing this.