Topic: Mathematics of generating an alternate chain (Bitcoin whitepaper). (Read 180 times)

tobasco

member

Activity: 61

Merit: 12

I've been looking at the equations from the bitcoin whitepaper. It gives the following probabilities of "catching up" from z blocks behind (with my 0.1 probability of mining a block) as follows:

Code:

q=0.1
z=0 P=1.0000000
z=1 P=0.2045873
z=2 P=0.0509779
z=3 P=0.0131722
z=4 P=0.0034552
z=5 P=0.0009137
z=6 P=0.0002428
z=7 P=0.0000647
z=8 P=0.0000173
z=9 P=0.0000046
z=10 P=0.0000012

However, if I want to replace the top block in the chain, catching up isn't going to be enough as I need to build a longer chain for other nodes to adopt.

So would it by correct to say my probability of replacing the top block in the chain would be:

Code:

z=2 P=0.0509779

Because I need to build a chain one block longer than the number of blocks I need to catch up with. Is that correct?

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