5 ms·
>>Seems pretty straightforward to me. Let's say you play a game with an edge where you win 2x your money 99% of the time. But if you lose once, you lose all you
by bluecalm 9y ago
>>Seems pretty straightforward to me. Let's say you play a game with an edge where you win 2x your money 99% of the time. But if you lose once, you lose all your money (1% risk of ruin). If you play this game 70 times, you are very likely to end up ruined
No one sane plays a game like that with all their money on the line. This is not because there are future bets available but simply expected utility of such a bet is negative. If you play for example with constant sizing your risk of ruin is higher than 0 but lower than 1. It's very often very close to 0.
>>It’s a lot like smoking. One cigarette won’t kill you, but add up the probability cigarette after cigarette, pack after pack, year after year and the probability starts to skyrocket.
But it's not like that. Risk of ruin doesn't skyrocket even if your plan is to make infinitely many bets. That is unless you do something very silly like double the bet amount every time you win.
- cardmagic 9y agoFirst of all, some people do play games like that. But put that aside for a moment because it’s immaterial. Look at what Taleb is essentially saying: if there is a chance you will be ruined, and you play long enough, you will eventually be ruined. Even if that chance is 1%, probabilities add over time. 1.0170 = 2. If the chance of ruin is 1% then after 70 plays the chance of ruin is 100%.
- bllguo 9y agoWhat kind of math is that? In your contrived example it should be 1 - .99^70. It's hard not to question your background in probability when you're involving 1.01 and 2..
- cardmagic 9y agoNice ad hominem attempt, but even though I accidentally switched a minus for a plus, the point the math teaches is the same: risk of ruin accumulates with the number of bets. For more information check "Risk of Ruin" https://en.wikipedia.org/wiki/Risk_of_ruin https://en.wikipedia.org/wiki/Risk_of_ruin
- bluecalm 9y agoYou are assuming people are betting their whole bankroll on one bet. No one remotely sane does that. If you do something like betting constant amount then risk of ruin is often very close to 0 (and always less than 1 if you have an edge).
- cardmagic 9y agoYou are wrong twice there... sane people make that bet every day by smoking (limited upside gain, risk of ruin loss) and by taking many prescription medicines that have side effects including death. Using a cell phone is taking that bet. You are betting that 50 years of cell phone exposure won't cause brain cancer. Nobody knows for sure yet, nobody has had cell phones for 50 years. I'm not saying it will or it won't cause cancer. I don't know. But it has the possibility of risk of ruin. Second, constant amount betting does have risk of ruin even with an edge. Take a fair coin flip where you start with $500 and get $51 for heads and lose $50 for tails. A clear edge with a constant betting amount. In 100 flips, you have a 27.23% chance of ruin. For more information consult the concept of "Gambler's ruin" https://en.wikipedia.org/wiki/Gambler%27s_ruin https://en.wikipedia.org/wiki/Gambler%27s_ruin
- tinymollusk 9y agoHow much should you bet to never be ruined but maximize the long term expected value of your bets?
- tensor_rank_0 9y agohttps://en.wikipedia.org/wiki/Kelly_criterion https://en.wikipedia.org/wiki/Kelly_criterion
- scarecrowboat 9y ago>> No one sane plays a game like that with all their money on the line. Already mentioned in another comment, see LTCM as a prime example: https://en.wikipedia.org/wiki/Long-Term_Capital_Management https://en.wikipedia.org/wiki/Long-Term_Capital_Management
- smogcutter 9y ago>> No one sane plays a game like that with all their money on the line. It's essentially the game we played with the housing bubble.