That sounds like a big mistake, not a small mistake! :grin:

I agree, and retract my guess. I’m gonna have to wait for someone else to correct me, though.

There is a small mistake in (b).  If x approaches 0.5, your solution would imply that Alice wins with near 100% probability.

SimpleStacker

a. If Alice hides the block, hash power is now directed separately at two chains. Alice is mining on C-A while Bob is mining on C. What is the expected time until Alice finds C-A-A, and what is the expected time until Bob finds C-B?

The expected time for Alice to find C-A-A is 

The expected time for Bob to find C-B is 

b. What is the probability that Alice finds C-A-A before Bob finds C-B? Hint: Look up Poisson processes and competing risks.

The approximate probability that Alice finds C-A-A before Bob finds C-B is 

math

bitcoin

Bitcoin Math Puzzle #002: Selfish Mining Pt. 2

> a. If Alice hides the block, hash power is now directed separately at two chains. Alice is mining on C-A while Bob is mining on C. What is the expected time until Alice finds C-A-A, and what is the expected time until Bob finds C-B?

The expected time for Alice to find C-A-A is $$\frac{10 min}{x}$$.
The expected time for Bob to find C-B is $$\frac{10 min}{1 - x}$$.

> b. What is the probability that Alice finds C-A-A before Bob finds C-B? Hint: Look up Poisson processes and competing risks.

The approximate probability that Alice finds C-A-A before Bob finds C-B is $$\frac{x}{1-x}$$.