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Use a small board, make sure everything is working on a small board. It's int divide. But I'm going to explain today why it's not worth bothering to stop an examine at each move whether somebody has won. You'd have to know some probabilities. We've seen us doing a money color trial on dice games, on poker. And in this case I use 1. Indeed, people do risk management using Monte Carlo, management of what's the case of getting a year flood or a year hurricane. And so there should be no advantage for a corner move over another corner move. Critically, Monte Carlo is a simulation where we make heavy use of the ability to do reasonable pseudo random number generations. Because that involves essentially a Dijkstra like algorithm, we've talked about that before. Rand gives you an integer pseudo random number, that's what rand in the basic library does for you. So we make all those moves and now, here's the unexpected finding by these people examining Go. You'd have to know some facts and figures about the solar system. So here's a five by five board. So if I left out this, probability would always return 0.{/INSERTKEYS}{/PARAGRAPH} No possible moves, no examination of alpha beta, no nothing. But for the moment, let's forget the optimization because that goes away pretty quickly when there's a position on the board. Who have sophisticated ways to seek out bridges, blocking strategies, checking strategies in whatever game or Go masters in the Go game, territorial special patterns. So it's a very trivial calculation to fill out the board randomly. Now you could get fancy and you could assume that really some of these moves are quite similar to each other. So what about Monte Carlo and hex? So you might as well go to the end of the board, figure out who won. So probabilistic trials can let us get at things and otherwise we don't have ordinary mathematics work. A small board would be much easier to debug, if you write the code, the board size should be a parameter. And we want to examine what is a good move in the five by five board. That's the answer. And we fill out the rest of the board. The rest of the moves should be generated on the board are going to be random. And if you run enough trials on five card stud, you've discovered that a straight flush is roughly one in 70, And if you tried to ask most poker players what that number was, they would probably not be familiar with. You're not going to have to do a static evaluation on a leaf note where you can examine what the longest path is. So black moves next and black moves at random on the board. And that's the insight. I've actually informally tried that, they have wildly different guesses. Why is that not a trivial calculation? You readily get abilities to estimate all sorts of things. How can you turn this integer into a probability? One idiot seems to do a lot better than the other idiot. I have to watch why do I have to be recall why I need to be in the double domain. You're going to do this quite simply, your evaluation function is merely run your Monte Carlo as many times as you can. Because once somebody has made a path from their two sides, they've also created a block. I think we had an early stage trying to predict what the odds are of a straight flush in poker for a five handed stud, five card stud. So here is a wining path at the end of this game. And we'll assume that white is the player who goes first and we have those 25 positions to evaluate. And we're discovering that these things are getting more likely because we're understanding more now about climate change. Here's our hex board, we're showing a five by five, so it's a relatively small hex board. And then by examining Dijkstra's once and only once, the big calculation, you get the result. Given how efficient you write your algorithm and how fast your computer hardware is. And that's now going to be some assessment of that decision. So for this position, let's say you do it 5, times. Once having a position on the board, all the squares end up being unique in relation to pieces being placed on the board. That's the character of the hex game. Okay, take a second and let's think about using random numbers again. This white path, white as one here. We're going to make the next 24 moves by flipping a coin. So it's not truly random obviously to provide a large number of trials. I'll explain it now, it's worth explaining now and repeating later. {PARAGRAPH}{INSERTKEYS}無料 のコースのお試し 字幕 So what does Monte Carlo bring to the table? So it can be used to measure real world events, it can be used to predict odds making. So here's a way to do it. And you do it again. And that's a sophisticated calculation to decide at each move who has won. And then, if you get a relatively high number, you're basically saying, two idiots playing from this move. And then you can probably make an estimate that hopefully would be that very, very small likelihood that we're going to have that kind of catastrophic event. So there's no way for the other player to somehow also make a path. We manufacture a probability by calling double probability. So here you have a very elementary, only a few operations to fill out the board. So we're not going to do just plausible moves, we're going to do all moves, so if it's 11 by 11, you have to examine positions. You can actually get probabilities out of the standard library as well. Maybe that means implicitly this is a preferrable move. This should be a review. So we make every possible move on that five by five board, so we have essentially 25 places to move. So we could stop earlier whenever this would, here you show that there's still some moves to be made, there's still some empty places. The insight is you don't need two chess grandmasters or two hex grandmasters. So you could restricted some that optimization maybe the value. Of course, you could look it up in the table and you could calculate, it's not that hard mathematically. You could do a Monte Carlo to decide in the next years, is an asteroid going to collide with the Earth. That's going to be how you evaluate that board. And there should be no advantage of making a move on the upper north side versus the lower south side. But it will be a lot easier to investigate the quality of the moves whether everything is working in their program. But with very little computational experience, you can readily, you don't need to know to know the probabilistic stuff. Instead, the character of the position will be revealed by having two idiots play from that position. You're not going to have to know anything else. So it's not going to be hard to scale on it. All right, I have to be in the double domain because I want this to be double divide. So it's really only in the first move that you could use some mathematical properties of symmetry to say that this move and that move are the same. And these large number of trials are the basis for predicting a future event. And indeed, when you go to write your code and hopefully I've said this already, don't use the bigger boards right off the bat. And the one that wins more often intrinsically is playing from a better position. And at the end of filling out the rest of the board, we know who's won the game. And you're going to get some ratio, white wins over 5,, how many trials? That's what you expect. So you can use it heavily in investment. So it's a very useful technique. It's not a trivial calculation to decide who has won. White moves at random on the board. Turns out you might as well fill out the board because once somebody has won, there is no way to change that result. Filling out the rest of the board doesn't matter. Sometimes white's going to win, sometimes black's going to win.