How you will go bust in favorable bet by N N Taleb - https://youtu.be/91IOwS0gf3g
I like the presentation style though, and the allusion to Shannon’s theorem although I didn’t quite grasp the connection.
That said, growth is pretty close to optimal even for smaller wagers. This plot shows growth rate as a function of wager size: https://www.wolframalpha.com/input/?i=plot+log%2850+-+x%29*0...
The other side of this is Shannon's Demon: a sort of crappy game can be made into a profitable one by sizing it properly (and rebalancing).
I think it would be intuitive for anyone that you could lose the first few rounds despite there being very favourable probabilities. If you really do go all-in, you could lose it all on the first round. But he's using an example of going "just" 80% in.
I think the part that's unintuitive for many people is that the probability of going bust increases the more rounds you play. Most people (myself included, perhaps) would naively expect that a favourable game would always have positive return as the number of plays increases. That's a mental failure to account for the fact that the game ends if we lose everything.
The counterintuitive result is because if you put 80% in each time, you could lose 99.97% after 5-straight losses or 99.99999% after 10-straight losses. The more you play, the more likely you are to eventually hit N consecutive losses and, therefore, go bust.
I have to concede that I don't know who would start from a place where they think betting 80% of the farm on each play is a sane strategy. Then again, we've all heard of founders who re-mortgage the house to fund their startup so...
My two examples were based on the idea that there’s some limit on how we can divide the original bet. For example, if a person starts with $10 and loses 99.97%, they have nothing left because rounding. Likewise for losing 99.999% of $1000.
In hindsight, though, the risk of consecutive losses wasn’t the point of the math. As you point out, the asymmetry is the problem. Loss occurs over time even with intermittent losses.
Here’s an example of how to half $100 in capital, despite a 70% win rate.
$100.00
$ 20.00 (L)
$ 36.00 (W)
$ 64.80 (W)
$ 12.96 (L)
$ 23.33 (W)
$ 41.99 (W)
$ 75.58 (W)
$ 15.12 (L)
$ 27.22 (W)
$ 49.00 (W)
. . .