Am I missing something? It doesn’t seem counterintuitive to me that repeatedly making an all-or-nothing bet with a non-zero chance of losing will eventually cause my expected value of capital to go to zero.
I like the presentation style though, and the allusion to Shannon’s theorem although I didn’t quite grasp the connection.
As others pointed out, it's not all or nothing. The specific example he was using was that you have that p = 0.7 game and you invest 80% of your wealth on each round.
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...
I'm not sure I really agree with the entire concept of "going bust" in these terms. To nit pick, you don't go bust if you lose 99.97% of your money. The real point is from whereever you start 5 losees will take away 99.97% of your money and it's asymmetrical- after those 5 losses you don't need 5 wins to make back your original sum of money because now your wealth is much smaller so you need far more consecutive wins to regain your wealth. It's counter intuitive because most people don't really think about the implications that you're betting a fraction of your wealth and your wealth at each timestep is a compounded function of the previous timesteps. They think of wealth as a constant where it's not.
You’re totally right and my rationale was mistaken.
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.
I forget what he said in the video, but generally this thing can be a little surprising because even a pretty decent looking bet can blow you up with high probability if you size it wrong.
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).
Right, I don't think that's the part that's counterintuitive. It's the claim he makes "if someone offers you a bet 70% chance to win a dollar, 30% loss, it's better not to take it in some cases" is what is counterintuitive to people.
Probably depends on your aversion to losing it all. If it's a dollar go for it. If it's 100 dollars, again, take the bet. If it's your life savings of 50000 dollars and going to 0 would be worse for you than 70/30 doubling your money, you don't want to go for it.
Sure, much like the Kelly criterion would tell you. If your life savings are $50,000, and someone offers you an even odds bet but with a 70 % chance of winning, you get optimal growth by wagering $20,000. However, that assumes you'll get a large number of similar offers so that you can make your losses back later if you get unlucky now.
