So fun fact about me, back in college I spent about a year and half with poker as my only source of income. It helped that I was living with my parents still so I didn't have to make that much for it to work, but I never asked them for money during that time and was able to do things like take a trip out to Vegas for one of the $1500 events in the WSOP. I wish I still had more time to play but it's a pain in the ass to drive two hours to a casino and none of the large poker sites are open to US customers still. Still though, the time I spent studying and playing poker had a profound effect on how I make decisions and view the world.
A lot of us view the world as deterministic, thing that doing A will cause B to happen. However, this is not how things are. The world is actually probabilistic. Doing A will likely cause B, but there is a chance that C, D, or E could happen too. Even something that seems simple, like pushing on a door to open it, could have different outcomes. Maybe I try to open it and there is a gust of wind that stops me. Or a box behind it I can't see. Or I hit a person there. Or suddenly the Higgs Field stops and all of existence disintegrates (just had to open that door huh?). Some of these are so unlikely that it's silly to include them in your calculation on whether to open that door, but you should know they are there.
In poker you constantly have to make choices that depend on a probability of outcomes. I know that if my opponent is drawing to a flush on the flop that he's got about 2:1 odds of getting there by the river. I know that if my opponent has a lower pocket pair than me pre-flop that there's about a 12% chance he wins anyway. You don't win in poker by being lucky or being good at bluffing or by avoiding bad beats, you win by consistently making the choice that is best suited to your situation and the current odds. The measure of whether or not your choice is a profitable one is called your expected value.
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Expected value is the sum of every possible outcome multiplied by the results of that outcome. For a simplified example, lets go back to that flush draw. Lets say I have KhQh and my opponent has AsAd. There's $20 in the pot, the flop is 5h4h8c. I act first and bet $15, my opponent goes all in for $65 total. The pot is now $100 (20+15+65) and I have to call $50 more. What do I do? Well with two cards to come my odds of hitting the flush and winning are roughly 36%. So my choices are to fold and lose nothing further (the money already in the pot is sunk cost), or call. 64% of the time I call and lose, so that portion of it is (-50x64%) = or -32. 36% of the time though I win what's currently in the pot, so that is (100x36%) or 36. 36-32=4, so on average I would expect to make $4 by calling. Since 4 > 0, I should call, even though technically it's less likely that I'll win. Sorry you now have a headache from the mini math lesson.
Looking that the choice deterministically a person could potentially come away with a lot of misconceptions about the choice. I played a hand is supposed to lose, therefor I made a bad play. If I win I just got lucky. Or maybe you think because I made that choice and won you should always do that, even though if the pot was 90 instead of 100 it would have been a bad call. See looking at the world from a deterministic point of view often can lead to results oriented thinking. In deciding whether a choice was good or bad, the actual results of that choice are irrelevant. Unless you miscalculated your odds, given the same set of circumstances you should always repeat the choice that has the highest EV, regardless of past results. I bet there are a lot of people in the cryptosphere who made a lot of money and think they are geniuses because of it. Really though the odds were never that great for bitcoin to take off the way that it did and just because it worked out once does not mean it will work out again. A lot of people ended up broke during the dotcom boom too.
Of course not everything is valued in dollars either. However, that doesn't mean you can't use this outside of fiscal decisions. Everything you want in life, money, peace, happiness, security, has a value that you place on it. Every choice you make has a probability of outcomes that will either given you some value in some, or take away in others. You may have to decide if you want to spend money to take a vacation. Is the loss of money going to be offset by the gain in happiness? Maybe you have an amazing time and it is, or you have food poisoning the whole time and it's not. But that choice should always be made on what you think the EV of that choice is.
The problem with this thinking, it's way easier said than done! You have to somehow figure out the probability of your outcomes, and then the value of those outcomes. If you make a mistake then what seems like a good choice may very quickly end up a bad one. On top of this we tend to have a bias towards towards causal relationships as well. Animals learn via causal relationships. Your dog does tricks because he thinks if he does A, he will get B reward. If I'm a rodent I don't have time to sit there and think what the odds are of the cat eating me, I just need to bounce ASAP. It's faster and simpler. It's also easier to apply as knowledge. A therefor B is concrete. A therefor B, but maybe also other things means more time processing, and I've already talked about how much your brain tries to conserve processing.
Probabilistic thinking however is needed to actually solve a lot of the complex problems we face, both personally and as a society. Let's take the hottest issue right now, gun control. People on both sides use deterministic thinking to make their arguments and discount the other one. Gun control will end in oppression and tyranny! People will find ways to kill without guns! Criminals will still find ways to have guns! Good guys with guns never stop anything! Mental Health is the real problem! Guns are only used to kill people! You're less safe with a gun than without one! All of these are factors that are sometimes true, and sometimes not. People stick to one thing and say this will happen, and that's why we should make a choice.
None of that is right though, you have to take a look at ALL of the possible outcomes and how likely they are and then make the decision based on that. It actually doesn't matter if later on there are undesirable outcomes, what matters is the choice that was made gives you the best chance to be successful. Unfortunately it's not very easy to sell people on a solution when your answer is "it depends." Probability however doesn't really care in a specific instance what you want or what's best or how hard you try. However, if you can accept the variance and choose whatever gives you the best EV, you will always come out ahead in the end (except, you know, the .0000001% of the time where you don't).
