  We present three very simple variants of the classic Heads or Tails game
using chips, each of which contributes to our understanding of the Bitcoin
protocol. The first variant addresses the issue of temporary Bitcoin forks,
which occur when two miners discover blocks simultaneously. We determine the
threshold at which an honest but temporarily ``Byzantine'' miner persists in
mining on their fork to save his orphaned blocks. The second variant of Heads
or Tails game is biased in favor of the player and helps to explain why the
difficulty adjustment formula is vulnerable to attacks of Nakamoto's consensus.
We derive directly and in a simple way, without relying on a Markov decision
solver as was the case until now, the threshold beyond which a miner without
connectivity finds it advantageous to adopt a deviant mining strategy on
Bitcoin. The third variant of Heads or Tails game is unbiased and demonstrates
that this issue in the Difficulty Adjustment formula can be fully rectified.
Our results are in agreement with the existing literature that we clarify both
qualitatively and quantitatively using very simple models and scripts that are
easy to implement.
