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I was under the impression that "shoot the missile down with another missile" style ICBM defence doesnt work, and that everyone already knows this.

Doesn't Israel shoot down incoming missiles with other missiles all the time? Or are you speaking specifically of ICBM-only scenarios?

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Yeah ICBM’s, which are hypersonic. Pretty much nothing can reliably guard against a first strike. Maybe a retaliatory strike.

And that's the only reason MAD work. If one side was even about to be able to reliably defend itself against a first strike, the other would have no choice but to strike while they still can.

With enough mid course interceptors, you can. That's simple math

Even Israel's system is really poor (240/690 in may) and it doesn't try to shoot down hypersonic missiles.

If one of these 240 was aimed at your family house you'd be glad it was intercepted though.

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