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According to Wikipedia, the US and Russia have close to 8,000 nuclear warheads each. Other known nuclear powers, the UK, France, China, India, Pakistan and Israel has a couple of hundreds each. The Cold War numbers were even higher, at some point the US and the USSR peaked at more than 30,000 nuclear warheads.

What is the rationale of having such a large number? Nuclear weapons cost a lot to maintain and secure, so the benefits must be huge to justify this cost.

Given the devastating effect of nuclear attacks, after a couple of dozens attack the enemy country would be decapitated, and the entire Earth would probably be subject to dangerous radiation, which would make further nuclear attacks irrelevant or undesirable, right?

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    youtube.com/watch?v=ybSzoLCCX-Y – cpast Jan 19 '15 at 5:35
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    "after a couple of dozens attack ... the entire Earth would probably be subject to dangerous radiation" Well, we've already exploded over 2,000 nuclear weapons, at least 500 of which were in the atmosphere, and it's had very little effect on the Earth's habitability. – endolith Dec 25 '16 at 0:48
  • I would guess that the politicians in favour of nuclear weapons have not seen The War Game, nor Threads. – sampablokuper May 28 '17 at 22:05
  • It sure makes you wonder when countries like the Soviet Union, Russia, and China are the reasonable ones. But we're always told, through our propaganda outlets, like the media, that the U.S is the good guys. – dan-klasson Dec 15 '19 at 18:37
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  1. Not all nukes are the same. Nuclear weapons are designed for specific purposes. There are different launch systems like ships, submarines, intercontinental missiles, ground-based mobile launch systems, large bombers, small fighter-jets and even systems which can be carried by infantry. Each of these systems needs their own nukes when you want all of them to be ready for a strike at all times. And for most of these launch systems there are nuclear warheads with different yields or specializations.

    Having a stockpile of a wide variety of nuclear weapons gives a state a much wider range of option not only if but how they want to perform a nuclear strike.

  2. You need to be aware that the target might have defensive capabilities and might be able to intercept (certain kinds of) nuclear missiles in flight. To threaten such a state, you need to have the option to fire a lot more missiles than they can intercept.

    "So, you say you have enough SAMs stationed around your capital city to intercept a hundred ICBMs at once? No problem, then we send 200."

  3. When the enemy performs a nuclear first strike, their primary goal will usually be to make a counter-strike impossible by obliterating all your nuclear capabilities. A possible counter-strategy is to have so many nuclear weapon systems that it is unlikely to destroy them all before you can perform a counter-strike.

    "Even when you destroy 99% of our nuclear weapons, the remaining 1% can still bomb you back into the stone age".

  4. Another reason is having room for negotiation when it comes to bilateral disarmament agreements. A-missile-for-a-missile is a great deal when you have twice as many as the other side.

    "You have 8000 missiles and we have 10000. You are right, this is madness. Let's say we both agree to a fair deal and each get rid of 8000 missiles... What? You want us to trash more of ours than you trash of yours? That hardly seems fair, does it? But maybe we could be persuaded. Let's talk about those nice oil fields in front of your coast...

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    There's also added stability up to a point with more weapons. If you have a dozen nukes, you could find yourself in a situation where you have to use them or lose them. If you have thousands, you're much less likely to be in that situation, and can pull off a "no first use" posture. – cpast Jan 19 '15 at 18:08
  • Neither the USA nor Russia would "survive" 100 nuclear bombs in their 100 largest cities. And neither has any defense against these. So the value of having more than 100 weapons is purely strategic. – Martin Schröder Jan 22 '15 at 1:19
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    Regarding point 2, since nukes are primarily a deterrent, surely you don't need 200 live nukes, but rather, one live nuke and enough identical dummies that the odds aren't worth the risk? "You can intercept a hundred ICBMs at once? We'll send the nuke alongside 199 ICBMs with conventional warheads. 50:50 chance of annihilation. Feeling lucky?" – user56reinstatemonica8 Jan 27 '16 at 16:08
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Originally, the main reason for the Soviet Union and the US to stockpile so many weapons was to maintain what was called “mutually assured destruction”. The idea is that you need many weapons to ensure that enough of them survive a nuclear “first strike” to launch a “second strike” and obliterate your enemy. Both opponents thus know they would not gain anything by being the first to strike.

If you combine this with an obvious lack of trust and general dearth of reliable information on enemy capability, both sides end up engaging in an arms race, for fear of being taken over by the other.

Other nuclear powers don't operate under the same logic and therefore don't need to build as many nuclear weapons. India and Pakistan mainly try to deter each other and didn't need to partake in the global arms race. Similarly, Israel is presumably concerned about neighbouring countries and only need a few nuclear warheads to dissuade an invasion. I don't know much about China but I noticed that in many areas (space exploration, aircraft carriers, nuclear weapons…), they seem more interested in demonstrating and maintaining a basic capability than really competing with other powers. I guess India also plays a role in their calculations.

France is a more interesting case. It developed nuclear weapons primarily to gain an independent capacity to deter the Soviet Union, worried that the US might pull out of Europe in case of Soviet invasion. But France is a relatively small country, and simply could not compete with the two cold-war superpowers so it developed a doctrine called “dissuasion du faible au fort” (deterrance of the weak to the powerful). The idea here is that France has the capacity to destroy, say, ten Soviet cities, and that invading a small country like France is not worth sacrificing ten cities. Starting in the 1970s, it also relied on nuclear submarines to increase survivability.

Note that these considerations do not necessarily play such a big role nowadays. There is a whole lot of inertia in all this: contractors and politicians who lobby to keep each and every base, etc.

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    Excellent commentary on French nuclear policy; which is usually hard to come by. Fascinating. – LateralFractal Jan 22 '15 at 10:14
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Value

The value (and biggest cost) of nuclear weapons is strategic.

It has been claimed that "A country with nuclear weapons cannot be defeated [at an acceptable cost], but it can be destroyed." This statement is not quite true -- witness the outcomes of the Korean and Vietnam Wars, and the fates of the Soviet Union and South Africa. But even in these cases, the defeats were via domestic "loss of will to fight", not via military occupation of the United States, Soviet Union, or South Africa.

It has also been claimed that the only truly sovereign states are those that control their own currency, borders, and nuclear weapons (capable of being delivered against any power that might attack the state).

Economies of scale

The cost to maintain and secure a military base with one ICBM is not very different from the cost to maintain and secure a military base with 25 ICBMs, with a total of 200 MIRVs.

The secondary nuclear powers have generally used joint ventures (and/or espionage) to reduce their research and development costs. (The British received a great deal of R&D help from the Americans; the French and Israelis had a joint venture; the Soviets and Chinese stole important technologies from the Americans; the North Koreans helped the Pakistanis, who helped the Iranians; et cetera.)

Low kill ratios

As Philipp and cpast have pointed out, there are practical reasons to believe that 200 nuclear weapons are more valuable than just 10.

Many ICBMs are stored in hardened missile silos, and/or can be moved around. If a nuclear warhead detonates "too far" away from the (real) target, it might not destroy the target. For hardened missile silos, this "too far" distance is a tiny fraction of the distance that the ICBM has to travel. Thus, if a country has 25 ICBMs, an opponent might need hundreds of warheads to be confident of getting a "close enough" hit on every ICBM silo.

Limits on the devastation

During the era of atmospheric testing of nuclear weapons, the total strength of hydrogen bombs that were tested was comparable to hundreds of modern nuclear warheads. The radiation produced was acutely dangerous in local areas, and caused cancer risks downwind, but the overall effects were dwarfed by many other man-made disasters.

The Earth is big. Suppose a nuclear war devastated a 15-mile radius circle around 1,000 locations. That would be about 700,000 square miles, including many of the world's most heavily inhabited and/or industrialized areas. But it is only about 1 percent of the world's land area. Huge amounts of military and industrial infrastructure would survive, including some very pissed off survivors of those attempted decapitation strikes. Anyone fighting World War III needs to be prepared for a long war -- it might not be over right away.

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