It's not plus, it's either/or. If the alternatives you're comparing are attacking or not mining at all, the cost to attack is depreciation+electricity. If the alternatives are attacking or mining normally, the cost to attack is the lost mining revenue.

Will we see another big chunk bought this Thursday  

Yes. The integral is then over the constant function 1/(HX) which gives a result of 1 - Exp (-Y/(HX)).

e.g., for X=1, Y=1, H=4 this gives 22.1%.

As a reminder, these calculations are for the case that everyone's hashrate is fixed. If it grows over time, the numbers will be different (in the attacker's favor).

You make a good point about the multiplication. I thought bugs meant a bug in the multiplication code itself, not malicious usage of it.

Sure, http://www.wolframalpha.com/input/?i=1+-+Exp%28-Integrate%281%2F%284+t%29%2C+{t%2C+1%2C+2}%29%29

By the way, I've edited to add the simpler form of this expression, 1 - (1 + T/S) ^ (-1/H).

I parsed your scenario as Attacker:Honest = 1:4 and that the attacker never contributed to the honest network. If instead it's Attacker:Total = 1:4, so Attacker:Honest = 1:3 (but the attacker was honest in the first year), it's even higher, 17.0%.

It's actually quite intuitive. Suppose he tries a weaker strategy of trying throughout the year to find a single huge block that is equal to 2 years of the honest network's work. This is equal to 8 years of the attacker work, so the chance to find such a huge block in a year is 1/8 = 12.5%. But in his actual strategy he spends the first day trying to find a block equal to 1 year, in the second day a block equal to 1.03 years, and so on, so the probability is higher.

Needless to say, if instead of a huge block he tried to find several normal blocks, he would have no chance. The variance then is much lower so he can't luck out.

It is centralized. He's exactly right.

按淘宝的形式 只会更加降低时效性。 如果你经常上淘宝，会发现 买东西是件非常烦人的事情，，做淘宝卖家久的人，也会发现卖东西也是件非常烦人的事。、、

因为你会花大量的精力在挑选商品和讨价还价上。这就是为什么很多人现在不爱上淘宝 而喜欢京东 亚马逊的原因。

Actually, the probabilities for T = 10^3, 10^6, and 10^9 are 82.2%, 96.8%, 99.4%. Even for T=1 the probability is 15.9%.

I'm assuming of course the simplest case. In general, with a head start of S and a hashrate ratio of 1:H, the chance to succeed in time T is
1 - \exp ( - int_S^{S+T} 1/(Ht) dt )

你指的用户自定义付款时间和确认时间，这个方案不大可行，我们只能找1个买卖双方都认为合理的时间平衡点。

就好像淘宝买东西，拍下后，买家是有3天时间付款，否则交易关闭。 卖家那考虑到快递因素 ，给买家10天确认收货。补充的做法是他们可以通过旺旺渠道 商量延长确认收货时间

或许也可以通过绑定QQ号的形式，让双方自己协商延长时间。

I agree with this, but in the short term that which doesn't kill you makes you cheaper.

现在是网页端的声音提醒和 手机短信，短信是会有延迟，但我们交易状态的变化 网页端是实时的，不需要去刷新页面（类似微博）

有移动客户端的话，会有消息通知，可以在移动端完成付款和提交。

我们希望大家能提供更好的方案，对买卖双方都公平的方案，而不是质疑。

我们现在是10分钟，已经在开发移动客户端 可以通过移动客户端提交交易号和对交易确认或者拒绝结算。

这个系统目前还是适合即时成交用户，，比如不频繁操作的散户，矿工用户等。

so, huobi is going to be localbitcoins now?

币需要先充值的，人民币不需要

我们是结合股票交易系统的撮合机制和担保交易系统的结算机制。

比如你买1BTC 有可能是从1个用户手里买 也有可能从2个用户手里买。你不需要去找这2个用户，系统根据价格自动帮你撮合。你直接付款给这2个用户就可以。

That's the beauty of it - the result doesn't require exponential growth (though it does help a bit). If the hashrate of attacker and network is fixed to eternity, the attacker still has a chance of 100% to succeed eventually. This is because the harmonic integral diverges (the cumulative PoW increases linearly, so his probability of success each day decreases inversely linearly. The sum of this goes to infinity and this can be translated to 100% probability of success).

A positive lower bound on the hashrate ratio is a sufficient (though not strictly necessary) condition for this guarantee.

我们当然希望没人违规，

交易正常就是应该靠交易手续费生存发展，而不是靠免费吸引用户 背地用见不得人的手段去盈利，最终受害的是散户

看看目前的局面 难道和各交易所的所做所为没有关系吗？

Well, take care there— lots of things are busted without ever being noticed.

Yes, such as the OP_RETURN bug and the negative balance bug. The one suggested by OP, however, is too obvious comparing with the said ones.

Note cumulative, not last.

https://products.butterflylabs.com/homepage-new-products/1-th-bitcoin-miner.html

Aha! This was the information that I wanted. Thank you.