 That's for the problem. Where was the problem? Here's the problem. There's two people. Person A, person B. Person A has $1, person B has $2, person A when they're playing this game has a two-third probability of winning and person B has one third probability of winning. Whoever runs out of money loses. So here's the game. Begin. Begin game. Right? So if A wins, right? And B wins, right? The probability of A winning is two out of three. The probability of B winning is one out of three, right? I gotta make this tighter because we're gonna have more branches, right? Let me put this in the center. Right? Game begins. Game begins. Let's see if we can do this properly. So we got A and we got B. Two-thirds probability of winning, one-third probability of winning, right? Person A begins with $1. Person B begins with $2. Okay? Whoever runs out of money, the game's over, right? As soon as someone runs out of money, the game's over. Okay? Now, if person B wins, because person A only had $1, game over. Game over. We're here now, right? When person A wins, then you have, you can play again because person B now only has $1. Here's person A winning again and person B winning again, right? Probability of A winning and is two-thirds. Probability of B winning again is one-third, right? So if person A wins, person B is down to $1. If person A wins again, B is down to $0, A wins. Yeah, this is where the problem occurs, I think. Not sure if people are interested, but down the road, okay. Yeah, that one. So this one, game over. Game over. The issue is this, right? Because if you go down here and then you can play the next round, two-thirds and one-third, right? If this occurs, person B wins. Check this out. Person B wins. So person A had $1. He had $2. And then person B had $1. He had their back to the original. And then if person B wins again, game over. Game over. But if person A wins, then they're back to B having $1 and A having $2, right? So what happens here is this pattern is going to repeat. A and B, right? So what happens down the road here? Using this method, you can get an approximation of what the result will be. What was the end thing you wanted to know? Game ends if one is bankrupt. What is the probability of A winning the game? You can get close to it using this method. I don't know if you can get exact using this method. There's another way. There has to be another way to do this. But using this method lays down the problem in a way that you can actually visualize it. So probability of A winning is if you go down, because at some point the probability is so low that it really doesn't affect the it converges to a number, okay? Dr. Skill, hey, I have struggled with the Pythagorean theorem. I don't know if it's the correct name because I'm German. Yeah, Pythagorean theorem is the right-angle triangle, right? Let me know what you guys get for this. If you do this calculation, we'll do the Pythagorean theorem right now. I'm just gonna put the question out there for people, right? This is game over would be one-third. This would be two-thirds times two-thirds. Two-thirds times two-thirds, which is four-ninths, right? This one would be two-thirds times a third times a third, which would be two-twenty-sevenths. So you can add these guys up so far, right? What was the original question again? Wait a second, what? Game as a one. What is the probability of A? Oh, of A winning. Poop, just A winning. This is B winning, so we don't care about this one. This is also B winning, so we don't care about this one. So so far, probability of A winning is four nines, and then over here again, you can do this calculation would be two thirds times a third times two-thirds times two-thirds, and you get a number here, and you add that to that, right? And then you do a few more branches. What you're gonna find out it converges to a number. What is that number, right? That's gonna be eight eighty-nines, eight eighty-firsts, eight over eighty-one, eight over eighty-one. So eight over eighty-one plus four over nine, plus what? That doesn't matter. So this is gonna be here. Let's just add this up. Eighty-one multiplied by nine thirty-six plus eight, which is gonna be forty-four over eighty-one. What is that? Forty-four over. We need to take in limb or something. Yeah, we need to talk about limits for this. There's no doubt we're doing limits. So we have to come up with an equation, right? So this is saying right now, 54% approximately, right? How much higher is it gonna go? 54.32% .32%, right? So that's the lowest that is going to be. It's gonna look like higher. Looks like series. Yeah, it's gonna be a series. There's no doubt about it, right? Because that's what this is right now. So it's gonna be something along the lines of something plus something plus something plus something. And each one of these guys is gonna contribute less and less to the total, right? And then you do the limit of this. You come up with an equation, f of x. So limb, you're gonna come up with some kind of function as x, whatever the iterations are, approaches infinity, which is gonna be most likely permutations and stuff, right? Looks like 4 times n minus 1 over 3 to the power of n for n equals 2, 3. Who's Julian Assange? Is he a whistleblower? He is a journalist and a publisher. He's the guy that started off WikiLeaks and allowed whistleblowers to release information on the shenanigans of capitalist power. And he's being crucified in UK prison right now on behest of the US government. Okay, very important person, very important person. So the formula that Dr. Hang mentions is this. He's saying the formula goes like this. 4 n minus 1. Is that, I'm assuming the start is 3 to the power of n. Or is that supposed to be 4 to the power of, it could be that, for n, for n equaling 2, 3 or higher. But if it's higher, then the probability is gonna go zero, because it's gonna contribute less and less, right? So what's gonna happen is, as the n goes higher, the bottom is gonna explode, it's gonna become bigger than the top. So the contribution of these guys is gonna be less and less, right? Elder God, you got 57%. I'm rubbish. No, this is the lower bound. There's gonna be more, because we only went two levels on this, right? There's gonna be more coming in from this and this. So for sure it could be 57%. It's a sum, yeah. But just eyeballed it. Yeah, yeah. It's cool. It's cool. As far as Pythagorean theorem goes, let's do Pythagorean theorem last couple of minutes. Nice problem, by the way. Nice problem.