If the US or USSR had a 99.99% effective anti-nuke deterrent, would either side have launched a first strike

For the sake of clarity, here are some ground rules:

1. Anti nuke refers to stopping the opposing nuclear triad (sub based missiles, bombers, ICBMs, etc) , although stopping portable battlefield nukes may be another matter
2. This hypothetical nuclear deterrence is global in reach and applies to all allies
3. Depending on the time frame you choose, the secondary nuclear powers (France, China, etc.) are under the protection of their respective superpower ally
 
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