Although German overconfidence played a major role in the success of Allied cryptanalysts, there were many other factors at play. One of the most significant reasons for Allied success was that the Allies had much more to lose. Initially, Marian Rejewski cracked Enigma because the threat of a German invasion of Poland was extremely high. Whereas other countries such as France had given up on breaking the Enigma, the Polish had too much to lose should they fail. Rejewski and his team spent a full year creating a book full of all of the potential keys for the Enigma. When it became clear that a German invasion of Poland was inevitable, Rejewski and his team handed over their work to the British, in hopes that they might be able to use it as well.
As the Germans added features to the Enigma to strengthen its encryption, such as additional plug board options, the Allies had to step up their game. Once again, the Allies had too much to lose for them not to invest the time and resources into cryptography. For each message the British failed to decipher in time, thousands of lives could be lost. The message could be about the location of the next air raid, or where the German troops were planning to move. Should the Allies have been able to know this information in advance, they might have been able to evacuate areas or adjust their strategies. Therefore, it was incredibly important to them that they be able to break Enigma. As a result, despite some reluctance on their commanding officer’s part, cryptologists at Bletchley Park were eventually given enough resources for Alan Turing to create his Turing Machine; a machine that was reliably able to crack the daily settings for Enigma.
When the stakes are higher, people work harder. German overconfidence certainly helped the Allies to be more successful with their cryptography, however, without the imminent German threat it is unlikely that people like Marian Rejewski and Alan Turing would have had the dedication or the resources, respectively, to break Enigma. Without cracking Enigma, the war could have turned out very differently.