Please check my math!

[deathcode]

1 Th/s = Terahash per second. 1,000 Gh/s (1,000,000,000,000 h/s)

So, 56.53 Th/s (current network power) = 56,530 Gh/s
x1 Radeon 7970 = 0.68 Gh/s = ~$399
Total Network Th/s / Radeon hashing power = 83,132 GPUs
83,132 GPUs * cost per GPU ($350) = U$S 33,169,668.00

I know there's overhead involved, but potentially a government or central bank has way more chances to overtake bitcoin by investing only 25-30 million (to achieve 50%+ and dominate the network) in a few thousand mining rigs. ~10,000 rigs if you can fit 4-5 GPUs per motherboard. plus datacenter + electricity.
What's wrong with this picture?
I'm sure it can't be that easy...!!!
Where am I wrong?
Feel free to shred this theory to pieces, but show me why it wouldn't work.

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[Qoheleth]

I'm sure it can't be that easy...!!!

Why not?

The hashrate is still way too low to defend against a billionaire or a major government.

That shouldn't be a surprise - Bitcoin itself is still a very niche thing.

[Lethos]

It's not so much they couldn't do it, probably in the region of $50-100M once you factor in more of the costs.

1) Buying that many high end computer parts in bulk is a lot regardless of who you are.
2) You'd need a data center, a large one entirely to yourself (20-30MW power station), build or rent?
3) What be the point, if they wanted to crush it, it be more cost effective to do it within the legal system.

It's that they have a hard time doing the above unnoticed. Doing so without anyone tracing it back to them, would really not be worth the risk of damage it could do to them.

[ShadowOfHarbringer]

1 Th/s = Terahash per second. 1,000 Gh/s (1,000,000,000,000 h/s)

So, 56.53 Th/s (current network power) = 56,530 Gh/s
x1 Radeon 7970 = 0.68 Gh/s = ~$399
Total Network Th/s / Radeon hashing power = 83,132 GPUs
83,132 GPUs * cost per GPU ($350) = U$S 33,169,668.00

Your math is roughly correct, however you don't count the socio-psychological aspect of what would happen and how would people react if somebody started buying massive amounts of graphic cards.

1. Such event may not go unnoticed when you are a big entity (such as government). This could produce news like headlines "Government is going into Bitcoin mining", which would drastically increase not only Bitcoin value, but also create an influx of new users & miners into the network, which would result in increasing the difficulty massively.

2. Also, some governments (such as China's) may not like other governments (such as US), so if for example US governments starts fighting Bitcoin to save dollar, China's government may start their own Bitcoin mining program. China really doesn't like US dollar as a global currency, they just pretend they are happy with it.

3. After Bitcoin reaches certain critical point as a lot of people will be using it, government will not be able to shut it down without causing certain amount of civil disorder / protests etc. It may be a problem for them. It may be even completely impossible if Bitcoin becomes as popular as paypal.

However, my analysis could be wrong for some unexpected reasons.

[knightmb]

With that much money, you would not need build anything. Just buy all the Bitcoins that people are willing to sell, that alone would be enough to control it because there is a limited number that will ever be produced. The market values you read about have quite a bit of fluff to them since people having to be willing to purchase it for that amount, let alone sell it.

[NikolaTesla]

With that much money, you would not need build anything. Just buy all the Bitcoins that people are willing to sell, that alone would be enough to control it because there is a limited number that will ever be produced.

In that scenario, the remaining bitcoins would just become more valuable. Since they can be subdivided, the liquidity of the market wouldn't be affected at all.

On topic, i think it would be a good thing if MULTIPLE governments and corporate entities got involved in bitcoin mining; that would make a 51% attack even more difficult as long as there are enough entities involved and enough dispersion of the mining power.

[Dabs]

Why buy GPUs when the government can go ahead and create their own ASICs, or buy the entire next batch of ASICs from Avalon or BFL?

[MeatPopsicle]

Any of the TLA agencies have plenty of EEs on call who could whip up an ASIC in no time flat. The only thing preventing this, is that bitcoin is a drop in the bucket monetarily wise.

[spndr7]

[Also, some governments (such as China's) may not like other governments (such as US), so if for example US governments starts fighting Bitcoin to save dollar, China's government may start their own Bitcoin mining program. China really doesn't like US dollar as a global currency, they just pretend they are happy with it.

Governments could try manipulate and control generation and price of bitcoin,that seems a bit farsighted as of now,but it would be interesting when this happens. Governments/UN would be forming IETF like organisation to control and manage their own crypto currencies besides other global crypto currencies.

[wzl]

The NSA undoubtedly has this kind of processing power already.

I suspect that a good portion of the total network hashing power is from governments and large corporations with the resources to throw at this kind of thing.

[Remember remember the 5th of November]

Are you guys still talking about the government vs Bitcoin? This is 2013 so get over it! It's like the claim that the government knows about the existence of aliens aka 1993 Fox Mulder aka we are 2013.

[knightmb]

With that much money, you would not need build anything. Just buy all the Bitcoins that people are willing to sell, that alone would be enough to control it because there is a limited number that will ever be produced. The market values you read about have quite a bit of fluff to them since people having to be willing to purchase it for that amount, let alone sell it.

I don't think you understand economics very well. By the time the bank/government spends 1 million in bitcoing the price would hit 3 or four times the current price. Another 2-3 millions would be enough to double or triple the price again and by the time they try to buy with the remaining 5 million they might be able to get 10 bitcoins at the most... Of course these are made up numbers but I'm trying for you to understand the implications of trying to buy 30 million worth of bitcoin. It just won't be enough to dent the system.

I am afraid the misunderstanding is on your end.    If the value was 3 or 4 more times, who would actually buy it? And bitcoins are not infinitely divisible. Miners would be hurt the most because it would push them to mining for 0.0000001 transactions which would overrun the fees. From a mathematical standpoint, buying the larger amounts nets investment at the expense of the miners. It's not economics but mathematics that would rule out that scenario.

[oakpacific]

Exactly why the "ASIC is harmful to Bitcoin" talk is nothing but bullshit.

[jubalix]

Why buy GPUs when the government can go ahead and create their own ASICs, or buy the entire next batch of ASICs from Avalon or BFL?

I am sure Gov is ordering from BFL...

[ISAWHIM]

Why buy GPUs when the government can go ahead and create their own ASICs, or buy the entire next batch of ASICs from Avalon or BFL?

Or just seize them in legal issues... "taking ownership" of the machines... You know, "for national security reasons"... (Not because they are actually a threat, that would be an "excuse", to seize them.)

[Zaih]

With that much money, you would not need build anything. Just buy all the Bitcoins that people are willing to sell, that alone would be enough to control it because there is a limited number that will ever be produced. The market values you read about have quite a bit of fluff to them since people having to be willing to purchase it for that amount, let alone sell it.

That won't change much lol. Simple money supply tbh. Bitcoin would just be boosted through that one would think.