Why are forks in the Blockchain eventually resolved?
If we simplify and assume that each miner randomly guesses a hash (as opposed to being more systematic) and we discretize time, say into minutes, then each minute each miner is hoping to "roll" the right number. Let's say there are $N &gt; 1$ possible values only one of which is correct at each minute. Then, in a world with only two miners, each minute there is only a $\frac{1}{N^2}$ chance that both miners will roll the correct value. There's a $1-\frac{3}{N^2}$ chance that neither miner rolls the correct value. There is a $\left(1-\frac{3}{N^2}\right)^k\frac{1}{N^2}$ chance that both miners roll the correct value after exactly $k$ steps of both not rolling the correct value. The probability that they will both roll the correct value for the first time at the same time is then $$\sum_{k=0}^\infty\left(1-\frac{3}{N^2}\right)^k\frac{1}{N^2} = \left(\frac{1}{1-\left(1-\frac{3}{N^2}\right)}\right)\frac{1}{N^2} = \frac{1}{3}$$

So the odds of them rolling the correct value at the same time $m$ times in a row is $\frac{1}{3^m}$. With more miners, birthday problem aspects enter, but that won't change the exponential nature. (In fact, I don't think the birthday problem really comes into play since each miner still needs to get the correct value not just a value that matches another miner's.)

I'm pretty sure this is the idea the author had in mind. As you say, though, a malicious miner (a selfish miner) can withhold announcing blocks until they notice someone else announcing them. To account for that, you could instead consider (in the two miner world again) what the probability is that the malicious miner finds a block before the honest miner. If the miners are comparable, then that's presumably something like $\frac{1}{2}$. However, things are further complicated by the fact that when the malicious miner does find the correct value first, then that miner also gets a head start on finding the correct value for the next block. Nevertheless, for comparable miners, there is still a good chance that the honest miner will find a block first despite the malicious miner's head start. This reasoning starts to get into the selfish mining aspect I referenced in the comments.