Suppose one day you have sold all that you own, and it is in your pocket as you walk down the street, ten Bitcoin or ten million or whatever it may be.
Suppose that day walking down the street you run into a game, which in a provably fair fashioni offers you 2 in 3 odds to win double your wager back.
The question before you is, what should you do ? Should you press on or stop and play ?
The answer before you is that you should indeed stop and play.ii This notwithstanding any nonsense you may misrepresent as "morals" (such as "don't gamble") and so forth. In point of fact any game with a positive expected value is to be played, period.
So now, that question answered, you stop and play, which sprouts another question : how much should you wager ?
The answer is known as the Kelly criterion, which simply says that you should take your return, multiply it by the odds to win, subtract the odds to lose, and divide the lot by the return. That's the fraction of your money you should wager at any point on any +EV propositioniii. Numerically in our case, (.2/3 * 1 - 1/3)/1= 1/3. We have 66.(6)% odds to win, and 33.(3)% odds to lose, and this offers us a round and thus very convenient answer : at every juncture bet a third of your dough.
Why not bet it all ? Well, what happens if you do bet it all and lose ? You're screwed. And if you win... then you should bet again, right ? What if then you lose ? Still screwed. And if you win... it'll just take a little longer, but overall you're definitely screwed, because sooner or later that 1/3 chance will actualise and that's the end of you. So no, all in is not really a sane strategy, inasmuch as the only guaranteed result is you being screwed.
The Kelly criterion optimises long term gains, which is to say it guarantees that out of a flock of people in which you are the only one playing this way, you will actually have more money at the end of any number of rounds than the average of the rest of the flock. No matter how large the flock, and no matter what other strategies they employ, you'll be on average better off.
This has however sharply discounted that aforementioned cost of opportunity. Suppose you are fifty, and that fortune you're carrying with you is all your life's work, all you've ever made. All of it. The Kelly criterion may be a little too aggressive for you, seeing how it still makes it perfectly possible to lose ten years' worth of hard work in just a few quick seconds.
But what, on the contrary, what if you're seventeen, and that ten is the result of an hour's work mowing a lawn ? Well in that case... Kelly's too slow for you, because even if you lose a lot of your bankroll, you've really not lost so very much in real terms.
That's it : when you're young you want to take bigger risks, because you can easily afford to cover unfortunate turns of events. When you're old you want to take smaller risks, because you ain't covering anything anymore. In any case you wish to strictly play +EV games.
And your life, all of it, from end to end, is nothing but you walking down the street and ending in front of a proposed game.iv
- This "provably fair" is a term of art in the Bitcoin space, and the 2nd most important fundamental reason why fiat gambling has absolutely no prayer in the future, irrespective of what anyone may decree or clamor on the topic. The 1st most important fundamental reason is that Bitcoin gambling is much cheaper to do, and so even without that 2nd substantial jump in quality it'd still run fiat out of the marketplace. In any case : you're well advised to form a good understanding of what "provably fair" actually means, as a more easily digestible and accessible step to actually understanding Bitcoin whole. [↩]
- A counterargument could be constructed on the cost of opportunity - if you're on your way to getting married perhaps you'd be better advised to carry on, especially if the houri scorned is liable to send you off to meet the maker. [↩]
- If you're confronting a -EV proposition, the Kelly criterion comes out with a negative fraction, indicating you should bet the other way, which perhaps might mean you should just start your own stand next to the one you've encountered. [↩]
- And for what it's worth, Wall Street does no better than this, nor does it do anything else, for all the pretense. [↩]