I’m starting a series on essays on gambling and taking risks. The premise of the essays is that there are cases where it is optimal to take risks, and even to gamble, even if the odds are bad, and maybe even if the system is rigged.
I’ll start with a simple example, maybe even too simple, and progressively introduce mathematical concepts, and talk about the optimal betting strategies, depending on the odds and the goals.
Lets first consider an extreme scenario. Imagine that you have $100,000 in your bank account. Sounds pretty good, right? Now imagine that you have a terminal but curable disease, like skin cancer for example. To cure your disease, you can undergo an operation, with 90% guaranteed success, which costs $200,000. And for sake of the example, lets assume it is not possible to borrow or crowd-raise the remaining $100,000 for your operation.
Lets consider two options. This might be too trivial, but bear with me for a while. The first option is that you do nothing. In this case, you’ll live for some short time, until the disease wins. The alternative is for you to go to a casino, and bet all $100,000 on roulette, on red. This will result in you doubling your money with about 47% chance, or losing them with about 53% chance. But if you double your money you can afford the operation. In that case you have a total chance of 47% * 90% = 42.3% of coming out alive.
Now it is clear, that among these two options, the better one is to gamble, as it provides some chance to survive the disease. Of course, if we want to make this example more realistic, you might think of other ways to raise money for the operation, but then I’ll devise some other constraint which sounds realistic and leave only the options of gambling or not gambling, and still make gambling the better option.
My main point so far is to show that there exist situations in life where it really makes sense to gamble. Furthermore, I’ll show you that there are many of those situations, in all parts of life, when gambling is better than not gambling. I’ll go beyond gambling and into taking risks in general.