[Appeared in Journal of Difference Equations and its Applications, volume 25, issue 1 (2019), 56-63.]

First Written: Aug. 15, 2018;
Last update of this webpage: Nov. 23, 2018.

Using Wilf-Zeilberger algorithmic proof theory, we continue pioneering work of Meni Rosenfeld (followed up by interesting work by Cyril Grunspan and Ricardo Perez-Marco) and study the probability and duration of successful bitcoin attacks, but using an equivalent, and much more congenial, formulation as a certain two-phase soccer match.

Added Sept. 7, 2018: watch the lecture:

Added Nov. 4, 2018: Read Version 2
Added Nov. 11, 2018: Read Version 3

Maple packages

• Bitcoin.txt, a Maple package to compute probabilities associated with bitcoin attacks.

Sample Input and Output for Bitcoin.txt

• If you want to see a computer-generated essay about our subject, that was used to write the human paper,

  the input file generates the output file.

• If you want to see results of simulations, confirming the theoretical results of the article. We have the following

  • The probablity of the bad team scoring a goal, q, is 1/5, for n from 1 to 16 (for n more than 16 it FAILED since the prob. of the bad team winning is so low) run 10000 times
    the input file generates the output file.

  [Note, that YOU should get different outputs every time, since this is simulations]

• If you want to see the first 100 Rosenfeld polynomials that tell you the probability of a successful attack if the good guys accululated n coins, for n from 1 to 100

  the input file generates the output file.

• If you want to see the first 100 Georgiadis-Zeilberger rational functions that tell you the expected duration of the second phase if the case of a successful attack,

  the input file generates the output file.

• If you want to see the cut-offs for the number of good coins to mint in order to guarantee probability of a successful attack to be less than 1/10, 1/100, and 1/1000 for q=0.29,q=0.323,..., q=0.356, ... all the way to q=0.49

  the input file generates the output file.

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