Joshua Alexanderが朗読する、Alton Hardinの『Essential Poker Math, Expanded Edition』を聴こう。 I have never put much effort into being a better poker player it's just been entertainment for me kind of like playing golf or going to a movie. but it is also a lot more fun, the cards will always be subject to luck but I don't gamble anymore, I make educated decisions based on the probability not

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確率（probability）は、分数表記として表していて、分母を表示桁に丸めています。 Four Js,Qs,Ks w/A,J,Q,K 40 1/ [1/] 5 of a Kind 1/ 拙作のVideo Poker Dis-card Tutor（VPDT）への展開を考えると、最初の1枚が出現したときの戦略は、予め計算してある結果を表示する

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For example, the average probability of any quads in flush mode is 1/ approx. All values これが重畳して、例えば4リールがwildに変化すれば、ライン全てが5 of a Kindとなるjackpotとなるわけです。 このjackpot

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club a) How many different three-of-a-kind regular poker hands are there? 1 +++). b) Compute the Probability Q&A Library 54 4, ana 5P5. What is the

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Probability[pred, x \[Distributed] dist] x が確率分布 dist に従うという仮定の下で述語 pred を満足する事象の確率を与える． Probability[pred, x \[Distributed] data] x が data によって与えられた確率分布に従うという仮定の下で述語 pred を満足

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4カード(Four of a kind)が2回フルハウスとフラッシュが回程度 かなり4カード以上は Hand Probability Odds against ピンボールでおなじみのJackpotの語源ですが、Pokerの世界から来ているようです。プレイヤーが

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The 4/2 Poker Rule was created to allow players to quickly, and reasonably accurately, calculate their odds during a poker hand. 12 outs which using the Rule of 4 and 2 we can calculate very quickly that the probability of hitting one of our outs is 12 x 4 = 48%. The rule of 4 tends to get kind of inaccurate much above 10 outs, which is unsurprising if you look at this derivation since

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function. 確率論：実験、標本空間、事象、確率関数。 • Examples. (outfits - use of tree, poker hands). /4/ Essential Math. I. 2 Slide “where order matters”. • Slide Add title “ Probability”. • Slide 例年 → 年齢. /4/18 /4/ Essential Math. I. 4. • After one pair the most common hands are two-pair and a three-of-a- kind: ワンペアの次に、最も一般なハンドとはツーペアとス

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日本ではポーカーのサイト自体が少ないので、この機会にProbabilityを計算してみました。 テキサス 最上位がK-5の9通り*4色に、最上位＋1の1枚を抜いた46枚から2枚 36*46C2 = (). ・4 of a kind

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Amazon配送商品ならTexas Hold'em Poker Odds for Your Strategy, with Probability-Based Hand Analysesが通常配送無料。更にAmazonならポイント還元本が多数。Barboianu, Catalin作品ほか、お急ぎ便対象商品は当日お届けも可能。

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