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	<title>简单赢：赢，就是简单！ &#187; 翻译</title>
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		<title>算牌法巡讲：KISS-II算法</title>
		<link>http://www.jiandanying.com/archives/897</link>
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		<pubDate>Tue, 18 May 2010 02:50:19 +0000</pubDate>
		<dc:creator>站长</dc:creator>
				<category><![CDATA[21点算法|分析]]></category>
		<category><![CDATA[算牌方法]]></category>
		<category><![CDATA[翻译]]></category>

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		<description><![CDATA[First of all, KISS stands for “Keep It Short and Simple”, so we are not talking about the band or anything. This is actually one of the easiest systems to learn other than a peculiar and curious requirement for the 2 point cards. It is actually quite powerful as well with good betting and insurance correlations with a fairly nice efficiency as well. This is also a level I (single level or level one) card counting system, which tends to be the easiest to learn.

<span class="readmore"><a href="http://www.jiandanying.com/archives/897" title="算牌法巡讲：KISS-II算法">阅读全文——共2737字</a></span>]]></description>
			<content:encoded><![CDATA[<p>First of all, KISS stands for “Keep It Short and Simple”, so we are not talking about the band or anything. This is actually one of the easiest systems to learn other than a peculiar and curious requirement for the 2 point cards. It is actually quite powerful as well with good betting and insurance correlations with a fairly nice efficiency as well. This is also a level I (single level or level one) card counting system, which tends to be the easiest to learn.</p>
<p>KISS是“Keep It Short and Simple”的简称。这首先是一种简单易用的算牌法，除了对牌面2的处理有点特别意外。这也的确是一种很有效的算牌法，同时也属于是简单（Level 1）的算牌法。</p>
<p>This system was made popular in the book “Blackjack Bluebook II”, written by the author Red Renzey. The KISS II count system is formulated to make it simple for the user but it can be added upon to gain more of an edge over the house such as in the KISS III count system. There is actually a KISS I system as well but it is not taken as seriously and it is only used by players who barely ever play. Essentially, it is useless to serious card counters and blackjack experts.</p>
<p>Red Renzey的《黑杰克蓝皮书 II》（Blackjack Bluebook II），另这种算牌法广为人知。首先是KISS-I算牌法，但由于效果不佳，所以几乎没有人使用。然后是KISS-II算牌法，将在这里介绍。在KISS-II的基础上，后来又发展出了<a href="http://www.jiandanying.com/archievers/899">KISS-III算牌法</a>，以获得更好的效果。</p>
<p>The KISS 2 count improves as the number of decks decrease, so it works great with single decks. The only majorly complicated part of this system is that suit awareness requirement, particularly with the number 2 cards. You need to count 0 when you see a red two and count +1 when you see a black two. Of course it does not matter whether you choose to count the red or the black cards, as long as you are consistent with it through the whole deck. This is denoted in the indexes below as 0/+1 on the chart. The table below lists the count values assigned to each type of card in the deck.</p>
<p>KISS-II算牌法的效果随着牌副数的减少而增加，所以最好是使用在1副牌的牌桌中。它的最复杂的部分是关于牌面2的计数，它要求当出现的是红色的2时，计数值不变；出现的是黑色的2时，计数值+1（反之也可以）。在下表中用0/+1来表示。</p>
<div>
<table cellspacing="0">
<tbody>
<tr>
<th title="This is what value card is dealt or seen on the table from either the dealer, the other players at the table or you.">牌面</th>
<th title="For every card seen on the blackjack table, add this number to your overall count value.">计数值</th>
</tr>
<tr>
<td>2</td>
<td>0/+1</td>
</tr>
<tr>
<td>3</td>
<td>+1</td>
</tr>
<tr>
<td>4</td>
<td>+1</td>
</tr>
<tr>
<td>5</td>
<td>+1</td>
</tr>
<tr>
<td>6</td>
<td>+1</td>
</tr>
<tr>
<td>7</td>
<td>0</td>
</tr>
<tr>
<td>8</td>
<td>0</td>
</tr>
<tr>
<td>9</td>
<td>0</td>
</tr>
<tr>
<td>10</td>
<td>-1</td>
</tr>
<tr>
<td>J</td>
<td>-1</td>
</tr>
<tr>
<td>Q</td>
<td>-1</td>
</tr>
<tr>
<td>K</td>
<td>-1</td>
</tr>
<tr>
<td>A</td>
<td>0</td>
</tr>
</tbody>
</table>
</div>
<p>This is also an unbalanced count system, which is a little bit easier to learn and is more convenient as you do not need to do calculations and conversions between the running count and true count. Although you still need to do a quick calculation of your starting count value, which depends on how many decks you are using. Normally you multiply -2 by the number of decks to get your initial count. For example, in a six deck game, your starting count would be -12 before any cards are dealt. Once the count goes above zero, then it is better to gauge when to start betting. Normally at this point, your edge would be somewhere around 1% above the house edge or more.</p>
<p>KISS-II算牌法是非平衡算牌法，它还是比较容易掌握的，而且你也不需要在计数值和真值之间进行换算。<strong>这种算牌对于不同的牌副数，使用不同的初始值来开始计数，1副牌就是-2、2副牌就是-4、3副牌-6，依此类推，6副牌就是-12、8副牌就是-16。</strong>当计数值大于零的时候，就应该下注了，一般来说，此时你的优势将反超过庄家1%。</p>
<p>KISS II is great for beginners and works well even with the factor that you need to keep track of the suit with the 2 point cards. Just remember that when the count is high and positive, you should be increasing your bets and when the count is low or negative, you should lower your wagers and bet the minimum to prevent losing when the casino has an edge over the players.</p>
<p>KISS-II和适合初学者使用，你唯一要注意的就是关于牌面2的特殊处理。其它的就简单了，当计数值是正数且足够大的时候，你就要下注并适当加大你的注额；反之，就应该减少注额甚至不下注。</p>
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		<title>算牌法巡讲：KO算法</title>
		<link>http://www.jiandanying.com/archives/901</link>
		<comments>http://www.jiandanying.com/archives/901#comments</comments>
		<pubDate>Mon, 10 May 2010 06:43:53 +0000</pubDate>
		<dc:creator>站长</dc:creator>
				<category><![CDATA[21点算法|分析]]></category>
		<category><![CDATA[算牌方法]]></category>
		<category><![CDATA[翻译]]></category>

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		<description><![CDATA[KO, or also known as knockout, is a common system used by blackjack card counters. There are a number of other systems out there such as Hi-Lo, Hi-Opt 1 and Hi-Opt 2. The basic concept of card counting is to start at a reference point such as 0. When certain cards are shown on the table, you add or subtract to this number until the count is at a desired level that would give you a greater edge.

<span class="readmore"><a href="http://www.jiandanying.com/archives/901" title="算牌法巡讲：KO算法">阅读全文——共3059字</a></span>]]></description>
			<content:encoded><![CDATA[<p>KO, or also known as knockout, is a common system used by blackjack card counters. There are a number of other systems out there such as Hi-Lo, Hi-Opt 1 and Hi-Opt 2. The basic concept of card counting is to start at a reference point such as 0. When certain cards are shown on the table, you add or subtract to this number until the count is at a desired level that would give you a greater edge.</p>
<p>KO算牌法，也被称为Knockout算牌法，是算牌手常用的算牌法之一。除此以外，还有许多其它的算牌法，比如<a href="http://www.jiandanying.com/archives/891">Hi-Lo算牌法</a>、<a href="http://www.jiandanying.com/archives/893">HiOpt-I算牌法</a>、HiOpt-II算法牌等等，所有这些算牌法的基本概念都是：<strong>设定一个参考计数值，从初始值开始（比如0），当每一张牌出现后，在这个计数值上相应的加上或者减去这张牌对应的计数值；直到某一个数值范围，而在这个范围内，你将获得更多的优势（更大的胜率）。</strong></p>
<p>There are two different categories of card counting. One is a balanced system, where you start off at 0 and count the cards and should end up with a total of 0 when the last card is dealt. If the count isn&#8217;t 0, then you did it wrong! The other category is unbalanced card counting, where the end total is not necessarily 0. Knockout (KO) is an unbalanced card counting system.</p>
<p>算牌法可以分成两种，平衡的和不平衡的。前者是“由零开始，到零结束”；后者是“由零开始，非零结束”（或者“非零开始，到零结束”）。<strong>KO算牌法就是一种非平衡算牌法。</strong></p>
<h2>KO Card Counting Strategy</h2>
<p>KO or Knock Out strategy begins with the fact that when the whole deck is used up, the count should not end up being zero. Normally there are an equal amount of points that apply to certain valued cards, but in this case, we would give the seven cards a positive 1 count. When a seven is seen on the table, you are adding one point to your starting reference count of 0 to give 1 point now.</p>
<p>一般来说，算牌法计数值表会给不同的牌面平衡地赋值，但在KO算牌法的规则中，多了一个7被赋予+1，这也就导致了最终的计数值无法回归到零。</p>
<p>The Hi-Lo counting system is one where there are equal points that add up to 0 when the last card is dealt. KO Knockout gives the 7 card that extra point, so at the end of a deck of cards, your final count should be 4. This is because of the four 7 cards in the deck. Multiply the number of decks by 4 to get your final count when playing with multiple decks of blackjack cards. The reason for this small variation is the convenience in not having to make conversions to the true count value. Below is a table of what count number you should add when you see one of these cards being dealt.</p>
<div>
<table cellspacing="0">
<tbody>
<tr>
<th title="This is what value card is dealt or seen on the table from either the dealer, the other players at the table or you.">牌面</th>
<th title="For every card seen on the blackjack table, add this number to your overall count value">计数值</th>
</tr>
<tr>
<td>2,3,4,5,6,7</td>
<td>+1</td>
</tr>
<tr>
<td>8,9</td>
<td>0</td>
</tr>
<tr>
<td>10,J,Q,K,A</td>
<td>-1</td>
</tr>
</tbody>
</table>
</div>
<h2>Benefits of KO Card Counting</h2>
<p><strong>KO算牌法的优势</strong></p>
<p>The system is not that difficult to learn. For example, in the KO count table above, if a 7 card is seen, add 1 point to your total. If an 8 card is dealt, don&#8217;t add anything to the count and if an ace or ten point card is seen, then subtract a point. Keep in mind, you need to do this in your head and you have to pay attention to all the cards on the table, even the dealer and other player cards.</p>
<p>KO算牌法并没有那么难学，小于8的牌减去1、大于9的牌加上1，就这么简单。</p>
<p>The Knockout card counting system is designed to be easier on the player when trying to keep track of the true count and the running count. The running count is actually the important number here and it depends on how many decks are being used. The true count is the number that you are adding up in your head. To find the running count, just divide the true count by the number of decks being played. For example, if you have a count of +8 while playing with a shoe having 8 decks of cards, your running count would be converted to only +1.</p>
<p>（上文中的真值和计数值的概念搞反了，这里的翻译已修正。）在算牌法中有两个很重要的概念，一个是计数值、一个是真值。计数值是指从一盒牌第一张牌开始你在脑中按照算牌法要求计算的那个值；真值是用计数值处以牌盒中剩余牌副数的值。比如，计数值是+8，牌盒中还剩余8副牌，那么真值就是+1。</p>
<p>The benefit of this system is you don&#8217;t have to keep doing the running conversion. It is easy for novice blackjack players who are just learning how to count cards and there really isn&#8217;t much different between the Hi-Lo card system and the KO counting system either.</p>
<p>KO算牌法的优势是你不需要进行计数值和真值的转换（存疑？），对于算牌新手来说很容易使用。事实上，KO算牌法和<a href="http://www.jiandanying.com/archives/891">Hi-Lo算牌法</a>的区别并不大。</p>
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		<title>算牌法巡讲：HiOpt-II算法</title>
		<link>http://www.jiandanying.com/archives/895</link>
		<comments>http://www.jiandanying.com/archives/895#comments</comments>
		<pubDate>Sat, 01 May 2010 09:41:56 +0000</pubDate>
		<dc:creator>站长</dc:creator>
				<category><![CDATA[21点算法|分析]]></category>
		<category><![CDATA[算牌方法]]></category>
		<category><![CDATA[翻译]]></category>

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		<description><![CDATA[Hi Opt II is another card counting system used by advanced blackjack players. Like the Hi Opt 1 system, Hi Opt 2 is the second version of the highly optimum (efficient) systems. This one takes a little bit of work to get used to and provides slightly better odds than the other highly optimal card counting system. If you are planning on becoming a professional card counter and blackjack player, this method should be studied a little.

<span class="readmore"><a href="http://www.jiandanying.com/archives/895" title="算牌法巡讲：HiOpt-II算法">阅读全文——共4442字</a></span>]]></description>
			<content:encoded><![CDATA[<p>Hi Opt II is another card counting system used by advanced blackjack players. Like the Hi Opt 1 system, Hi Opt 2 is the second version of the highly optimum (efficient) systems. This one takes a little bit of work to get used to and provides slightly better odds than the other highly optimal card counting system. If you are planning on becoming a professional card counter and blackjack player, this method should be studied a little.</p>
<p>HiOpt-II是另一种常被高级玩家使用的算牌方法，是<a href="http://www.jiandanying.com/archives/893">HiOpt-I算牌法</a>的第二个版本。这种算法需要花点时间来掌握，但同时你能获得更高的胜率（相较于其它类似算牌法）。如果你决心做一名专业的算牌手，那么肯定要学习这种算牌法的。</p>
<p>One word of advice: Practice the Hi-Lo or KO card counting systems before using the Hi-Opt II method. Hi-Opt II has much more work involved but it truly doesn&#8217;t give you that much more of an edge. That small edge is golden when you are used to counting cards and trying to maximize the efficiency of your odds though.</p>
<p>建议：在学习HiOpt-II算牌法前，先练习掌握<a href="http://www.jiandanying.com/archives/891">Hi-Lo算牌法</a>或<a href="http://www.jiandanying.com/archives/901">KO算牌法</a>。HiOpt-II算牌法相对来说比较复杂，好像也没有为玩家增加多少优势；但要明白，对于21点游戏来说，任何一点微弱的优势，都是难能可贵的。</p>
<h2>Difference between Hi-Opt II and Hi-Opt I</h2>
<p>The major difference with Hi-Opt II is some cards are worth positive 2 or negative 2 count points per card. It is harder to keep track because you also have -1 and +1 valued cards to also keep track of. Another difference between the two systems is that you are counting the 7 and 2 point cards where the Hi-Opt I card counting system doesn&#8217;t. Both systems are balanced, meaning that when you start your count off at 0 at the beginning of the deck, you should have a final count of 0 at the end because the negative and positive counted scores cancel each other.</p>
<p><strong>HiOpt-II和HiOpt-I算牌法的区别</strong></p>
<p>最主要的区别是，在HiOpt-II算牌法中，有一些牌的计数值是-2或+2。再加上那些依然被记为+1、0、-1的牌，当然也就使得HiOpt-II算牌法会比<a href="http://www.jiandanying.com/archives/893">HiOpt-I算牌法</a>更难掌握。还有一个区别就是，在HiOpt-II中要记录2和7这两个原本在<a href="http://www.jiandanying.com/archives/893">HiOpt-I算牌法</a>中不需要记录的牌。但同样的，这两种算牌法都是“平衡”算牌法。</p>
<h2>Hi-Opt II Card Counting Strategy</h2>
<p>As with all card counting strategies, Hi-Opt II begins with the memorization of basic strategy. Basic strategy is a list of the “correct” moves to make for every combination of dealer hands to your hands to give the greatest mathematical edge. This edge will still not beat the house though, but this fine tunes your odds and lowers the house edge as low as possible. Next you implement your Hi-Opt II system and this will be the factor that beats the house edge when done successfully.</p>
<p>之前在《<a href="http://www.jiandanying.com/archives/893">算牌法巡讲：HiOpt-I算法</a>》中曾说过，<strong>所有的算牌法都是对基本策略表的补充。而仅凭基本策略表，玩家是赢不过庄家的，因为此时庄家优势依然为正数，只有辅以合理的算牌法并正确运用，玩家才可能战胜庄家。</strong></p>
<p>The next part of the strategy is to memorize the table below to become a Hi-Opt II card counter. This is one of the hardest systems because of all the different cards and count points to keep track of. In the Hi-Opt II count table below, each card drawn corresponds to a count point. You start your count off when the deck is shuffled and the first card is dealt. You not only need to watch what cards you have, you also need to count the cards that the dealer has and everyone else&#8217;s cards on the table in order to get a good prediction of what cards are still left in the deck.</p>
<p>下表就是HiOpt-II算牌法的计数值对应表了，这是几种难度最大的算牌法之一，因为你需要跟踪并计算每一张牌。</p>
<div>
<table cellspacing="0">
<tbody>
<tr>
<th title="This is what value card is dealt or seen on the table from either the dealer, the other players at the table or you.">牌面</th>
<th title="For every card seen on the blackjack table, add this number to your overall count value">计数值</th>
</tr>
<tr>
<td>2</td>
<td>+1</td>
</tr>
<tr>
<td>3</td>
<td>+1</td>
</tr>
<tr>
<td>4</td>
<td>+2</td>
</tr>
<tr>
<td>5</td>
<td>+2</td>
</tr>
<tr>
<td>6</td>
<td>+1</td>
</tr>
<tr>
<td>7</td>
<td>+1</td>
</tr>
<tr>
<td>8</td>
<td>0</td>
</tr>
<tr>
<td>9</td>
<td>0</td>
</tr>
<tr>
<td>10</td>
<td>-2</td>
</tr>
<tr>
<td>J</td>
<td>-2</td>
</tr>
<tr>
<td>Q</td>
<td>-2</td>
</tr>
<tr>
<td>K</td>
<td>-2</td>
</tr>
<tr>
<td>A</td>
<td>0</td>
</tr>
</tbody>
</table>
</div>
<p>So when you see a card, for example a 5, then add +2 points to your count total. If you get a ten card, then subtract -2 points from your count and so on. When the entire deck is used up, your count should be 0 as Hi-Opt II is a balanced card counting system.</p>
<h2>When to Bet in Hi-Opt II Card Counting</h2>
<p><strong>关于HiOpt-II算牌法的下注时机</strong></p>
<p>It is ideal to bet when many of the smaller cards are gone. A lot of high valued cards mean that your odds improve and this is the whole purpose of card counting by using the Hi-Opt II system. Therefore when many small cards are played, your true count becomes a large positive number. The higher this number, the more your edge increases and the more the blackjack house edge decreases. So it makes sense to bet more and often. On the other hand, a large negative running count means there are fewer ten cards and more small stiff cards in the deck, which decrease your edge and it makes sense to contract your betting. Card counting is great for indicating swings in “good” luck.</p>
<p>当发出的牌中小点数牌的数量远远多于大点数牌的时候，就是下注的好时机了。HiOpt-II算牌法的目的就是识别出牌盒中剩余牌的点数是否足够大，因为当越来越多的小牌被发出后，你的计数“真值”就会随之越来越大，你的优势也随之增加，相应的，庄家优势随之减少——这也是你下注并提高注额的时机。反之，则你就要减少注额、甚至不下注。<strong>其实，算牌法就是告诉你“好运气”是否来到了。</strong></p>
<p>We also need to recall an important piece of information. The actual true count is the one that you are counting in the game. You need to pay attention to the running count. You can calculate and find the running count by taking the true count and dividing that number by the number of decks in play. For example, a true count of +4 in a 4 deck game has a running count of only +1. So you need to make your betting decisions based on your running count.</p>
<p>要特别提醒你的是，要用“真数”来作为你的决策依据。<strong>所谓真数，就是将计数值除以剩余的牌副数得到的数值。</strong>比如，计数值是+4，剩余4副牌，那么此时的真数就是+1了。</p>
<p>Also, the aces have a zero count in this system but this is something to watch out for. The real strategy says you need to make some very small changes to the basic strategy to account for the aces not being counted. You still need to keep track of how many aces are being played as well but that blackjack topic is extremely advanced and involves some mathematics.</p>
<p>还有，在HiOpt-II算牌法中，尽管Ace是记为零的，但仍然要特别关注Ace出现和剩余的数量。实际上，这涉及到对基本策略表进行些微的改动。而具体的理由和方法，因为涉及到许多的数学计算，就不在这里展开了。</p>
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		<title>算牌法巡讲：HiOpt-I算法</title>
		<link>http://www.jiandanying.com/archives/893</link>
		<comments>http://www.jiandanying.com/archives/893#comments</comments>
		<pubDate>Tue, 20 Apr 2010 03:48:45 +0000</pubDate>
		<dc:creator>站长</dc:creator>
				<category><![CDATA[21点算法|分析]]></category>
		<category><![CDATA[算牌方法]]></category>
		<category><![CDATA[翻译]]></category>

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		<description><![CDATA[This type of card counting system is known by a few names such as Hi Opt I or High Opt. Basically this is short for “Highly Optimum” and is a very advanced system of card counting. This is one reason why it is sometimes called the Einstein count method. It is not much different than the Hi-Lo system and it is another one of the balanced card counting systems. A balanced system means that when you start your count off at 0, you should be able to end your count at exactly 0 when all of the cards are used up.

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			<content:encoded><![CDATA[<p>This type of card counting system is known by a few names such as Hi Opt I or High Opt. Basically this is short for “Highly Optimum” and is a very advanced system of card counting. This is one reason why it is sometimes called the Einstein count method. It is not much different than the Hi-Lo system and it is another one of the balanced card counting systems. A balanced system means that when you start your count off at 0, you should be able to end your count at exactly 0 when all of the cards are used up.</p>
<p>HiOpt-I算牌法也被称为High-Opt算牌法，这其实是Highly Optimun（最优化）的简称，是非常先进的算牌法之一。这也是卫生那么有人称之为“爱因斯坦”算牌法的原因。它和<a href="http://www.jiandanying.com/archives/891">Hi-Lo算牌法</a>很相似，而且也是“平衡”算牌法（由零开始，到零结束）。</p>
<p>Because of this system&#8217;s highly optimal characteristics, it should be providing you with some of the highest odds that you can achieve through card counting. It is pulling out and maximizing blackjack efficiency in the game. We recommend learning Hi-Lo counting first before understanding this method because of the steeper learning curve. The advantage is only slightly greater with the first Hi-Opt I card counting method and is best for advanced blackjack players. There are some people who would disagree and swear by this system of card counting. I guess it just depends on what the type of player is and other elements in the game.</p>
<p>由于HiOpt-I算牌法高度优化的特点，理论上它可以很明显地帮助你提高你的胜率，不过我们还是建议您先学会<a href="http://www.jiandanying.com/archives/891">Hi-Lo算牌法</a>再来学HiOpt-I算牌法。</p>
<h2>Hi-Opt I Card Counting Strategy Guide</h2>
<p>The foundational aspect of all card counting strategies is to supplement them with the blackjack 21 basic strategy. The basic strategy is a list of what moves you should make to give you the the most optimum mathematical advantage. It tells you the “correct” move to make when given a combination of dealer and player hands. After you have this down, you will be playing the most efficient game and making all the perfect moves.</p>
<p>所有算牌法的目的都是为了对21点的基本策略表进行有效的补充。所谓基本策略表，就是一组预先计算好的结果表，告诉你在任一种庄家和玩家的牌面组合情况下，你应该采取的“正确”动作是什么，以帮助你取得最大的（理论上的）胜率。当你搞定了这些，那么你的每一把牌都将按照“最佳”步骤执行，从而获得更高胜率。</p>
<p>The next step is to implement the Hi-Opt I system to make the house edge flip over to your edge. Each card is assigned a count value. So when a card appears on the table, you add or subtract to your total count depending on what the card is. Keep in mind that you need to keep track of everyone&#8217;s cards, including the dealer and all the other players. It is best to wait for the deck to be shuffled and then start your count at 0. When the deck is all used up, the count should again be 0 at the end. A list of count values per card in the Hi-Opt 1 method is shown below:</p>
<p>接下来就要真正学习HiOpt-I算法了，通过它你可以将原有的庄家优势减少，甚至令你的优势超过庄家的。同样的，这种算法为每一张牌面赋予一个计数值，当一张牌被翻出后，你就要相应的加上或者减去对应的计数值。你要记录桌面上的每一张牌，包括庄家的以及其他玩家的，当然，计算工作要很隐蔽地在心中进行。最好是在一盒牌刚开始的时候开始计数，应该这时候的计数初值就是零；而当一盒牌都用尽的时候，你的计数结果也应该同步地归零才是。下表就是HiOpt-I的计数值表：</p>
<div>
<table cellspacing="0">
<tbody>
<tr>
<th title="This is what value card is dealt or seen on the table from either the dealer, the other players at the table or you.">牌面</th>
<th title="For every card seen on the blackjack table, add this number to your overall count value">计数值</th>
</tr>
<tr>
<td>2</td>
<td>0</td>
</tr>
<tr>
<td>3</td>
<td>+1</td>
</tr>
<tr>
<td>4</td>
<td>+1</td>
</tr>
<tr>
<td>5</td>
<td>+1</td>
</tr>
<tr>
<td>6</td>
<td>+1</td>
</tr>
<tr>
<td>7</td>
<td>0</td>
</tr>
<tr>
<td>8</td>
<td>0</td>
</tr>
<tr>
<td>9</td>
<td>0</td>
</tr>
<tr>
<td>10</td>
<td>-1</td>
</tr>
<tr>
<td>J</td>
<td>-1</td>
</tr>
<tr>
<td>Q</td>
<td>-1</td>
</tr>
<tr>
<td>K</td>
<td>-1</td>
</tr>
<tr>
<td>A</td>
<td>0</td>
</tr>
</tbody>
</table>
</div>
<p>The only difference between the highly optimal system and the high-low system is the two and ace cards have 0 points and you don&#8217;t count these. You are still counting low cards and high cards but not the middle cards. Most important, when you are using the High Opt I method, you should NOT be writing down your count. Counting should all be done in your head. Some players don&#8217;t realize this but you can be kicked out of a casino if they find out you are counting cards. People get confused because you are gladly welcome to bring in a basic strategy blackjack chart with all the correct moves. They let you do this because the casino still has the mathematical edge so they don&#8217;t care.</p>
<p>可以发现，HiOpt-I算牌法和Hi-Lo算牌法很相似，不同的地方就是HiOpt-I算牌法中，2和A的计数值都是0；其它都一样，你只要关心4张小点数牌（3-6）和4张大点数牌（10-K），其它的不需要。<br />
要提醒你的是，所有的算牌工作必须隐蔽，在心中计算，不能让娱乐场发现，否则，工作人员有权要你离开（不欢迎你）。有人会有疑问，为什么娱乐场不允许玩家算牌，却允许玩家大明大方地把基本策略表摆出来用。原因很简单，因为如果仅仅使用基本策略表的话，娱乐场是仍然保有其庄家优势的。</p>
<p>The other reason why Hi-Opt I card counting is an “advanced” system is because there are more things to keep track of and it&#8217;s more challenging to do correctly. The best thing to do really is to buy some cards at home and practice. Keep practicing carefully and then eventually have someone deal out the cards as fast as possible and see if you can count them all. With the High-Opt 1 method, you should always have a count of 1 when the deck is completely dealt, so you have some reference for practice. Another thing to keep in mind is the aces in this system are not counted and there is a <em>slight</em> change to the basic strategy because of this.</p>
<p> &#8230;&#8230;注意：因为HiOpt-I算牌法中没有被统计，因此这会导致基本策略表的些微变化。</p>
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		<title>牌桌上的坏策略 Bad Strategies</title>
		<link>http://www.jiandanying.com/archives/1037</link>
		<comments>http://www.jiandanying.com/archives/1037#comments</comments>
		<pubDate>Sat, 10 Apr 2010 09:49:56 +0000</pubDate>
		<dc:creator>站长</dc:creator>
				<category><![CDATA[21点算法|分析]]></category>
		<category><![CDATA[概率]]></category>
		<category><![CDATA[理论研究]]></category>
		<category><![CDATA[翻译]]></category>

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		<description><![CDATA[申明：以下文字及数据来源于网络，本站翻译，但并未对其中的数据进行验证。

Three popular bad strategies encountered at the blackjack table are: never bust, mimic the dealer, and always assume the dealer has a ten in the hole. All three are very bad strategies. Following are my specific comments on each of them, including the house edge under Atlantic City rules (dealer stands on soft 17, split up to 4 hands, double after split, double any two cards) of 0.43%.

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			<content:encoded><![CDATA[<p style="text-align: center;"><em><strong>申明：以下文字及数据来源于网络，本站翻译，但并未对其中的数据进行验证。</strong></em></p>
<p>Three popular bad strategies encountered at the blackjack table are: never bust, mimic the dealer, and always assume the dealer has a ten in the hole. All three are very bad strategies. Following are my specific comments on each of them, including the house edge under Atlantic City rules (dealer stands on soft 17, split up to 4 hands, double after split, double any two cards) of 0.43%.</p>
<p>在牌桌上最常见到以下三种坏策略——永不爆牌、模仿庄家、假设庄家的底牌是10——事实上，这三种玩家策略都是非常糟糕的。接下来我将分别来解说这三种坏策略；假设牌桌的规则是Atlantic City规则（庄家在软17停牌、最多分四手、分牌后允许加倍、任两张牌都可以加倍），此种规则的庄家优势为0.43%。</p>
<p><strong>Never bust</strong>: For my analysis of this strategy I assumed the player would never hit a hard 12 or more. All other decisions were according to correct basic strategy. This “never bust” strategy results in a house edge of 3.91%.</p>
<p><strong>永不爆牌</strong>：在这种策略下，玩家在硬12点及以上的时候就停牌了，以保证自己永远不会爆牌。可是，我计算的结果是，使用这种策略的话，庄家优势将提高到3.91%。</p>
<p><strong>Mimic the dealer</strong>: For my analysis of this strategy I assumed the player would always hit 16 or less and stand on 17 or more, including a soft 17. The player never doubled or split, since the dealer is not allowed to do so. This “mimic the dealer” strategy results in a house edge of 5.48%.</p>
<p><strong>模仿庄家</strong>：在这种策略下，玩家完全按照庄家的规则来决定要牌还是停牌，16点以下要牌、17点以上停牌、永不双倍下注、也用不分牌，完全和庄家一样。我计算的结果是，使用这种策略的话，庄家优势将提高到5.48%。</p>
<p><strong>Assume a ten in the hole</strong>: For this strategy I first figured out the optimal basic strategy under this assumption. If the dealer had an ace up, then I reverted to proper basic strategy, because the dealer would have peeked for blackjack, making a 10 impossible. This “assume a ten” strategy results in a house edge of 10.03%.</p>
<p><strong>假设庄家的底牌是10</strong>：&#8230;&#8230;这种策略下，庄家优势将提高到10.03%。</p>
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		<title>算牌法巡讲：Hi-Lo / High Low算牌法</title>
		<link>http://www.jiandanying.com/archives/891</link>
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		<pubDate>Fri, 19 Mar 2010 07:49:51 +0000</pubDate>
		<dc:creator>站长</dc:creator>
				<category><![CDATA[21点算法|分析]]></category>
		<category><![CDATA[算牌方法]]></category>
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		<description><![CDATA[The Hi-Lo card counting style is one of the most well known of them all. Other names for this style are also known as High-Low or Plus-Minus card counting. The Hi-Lo system was first invented by the mathematician Harvey Dubner and later improved by Professor Edward Throp, who was one of the founding fathers of card counting strategy. The Hi-Lo strategy is very easy to use by both novices and more advanced players. The high-low card counting method is the most commonly used type because of how easy it is to use and is most especially used by blackjack teams.

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			<content:encoded><![CDATA[<p>The Hi-Lo card counting style is one of the most well known of them all. Other names for this style are also known as High-Low or Plus-Minus card counting. The Hi-Lo system was first invented by the mathematician Harvey Dubner and later improved by Professor Edward Throp, who was one of the founding fathers of card counting strategy. The Hi-Lo strategy is very easy to use by both novices and more advanced players. The high-low card counting method is the most commonly used type because of how easy it is to use and is most especially used by blackjack teams.</p>
<p>大概Hi-Lo算牌法是所有算牌法中名气最大的了，它也被称为High-Low算牌法或+/-算牌法。这种算牌法最初是由数学家Harvey Dubner发明的，后来由Edward Throp教授（其被称为是算牌法之父）改进。无论是新手还是熟练的玩家，都可以很容易地使用这种算牌法，这也是黑杰克团队玩家的常用算牌法之一。</p>
<p>The first thing all blackjack players must do is learn and memorize the blackjack basic strategy and then complement this to the Hi-Lo method. You need to do this in order to maximize your edge as much as possible and this requires a nearly perfect game. The High-Low strategy starts by keeping track of every card that is seen on the table. This means watching what cards the dealer throws down and the cards that the other players have down as well. Each card is assigned a “count” value or point. A list of point values for each card is shown in the table below:</p>
<p>首先，你要学会并记住黑杰克的基本策略卡，然后结合入这个Hi-Lo算牌法，以最大可能地提升你的胜率。你要盯住桌面上出现的每一张牌（包括庄家以及其他玩家的），每一张牌都有一个点数，你要在心里快速地进行相应的加减运算。下表就是Hi-Lo算牌法的计数值表。</p>
<div>
<table cellspacing="0">
<tbody>
<tr>
<th title="This is what value card is dealt or seen on the table from either the dealer, the other players at the table or you.">牌面</th>
<th title="For every card seen on the blackjack table, add this number to your overall count value">计数值</th>
</tr>
<tr>
<td>2,3,4,5,6</td>
<td>+1</td>
</tr>
<tr>
<td>7,8,9</td>
<td>0</td>
</tr>
<tr>
<td>10,J,Q,K,A</td>
<td>-1</td>
</tr>
</tbody>
</table>
</div>
<p>The high-low card counting system is a balanced system. This means that when you start your count off at 0, you should end your count at 0 as well when every card has been seen and the deck needs to be shuffled again. This is because the lower five cards have +1 values and the upper five cards have -1 values so they cancel each other out. The best way to master this system is to keep practicing outside of the casino. You can learn to increase your counting speed by having yourself or someone quickly deal a deck of cards and you try to keep up with the count. Because this is a balanced card counting system, you should end up with a count of 0 at the end. If the count is not zero, then you know you have miscounted!</p>
<p>Hi-Lo算牌法是“平衡”算法（由零开始，到零结束）。你可以自己或者让朋友来快速地发牌，然后你开始计算相应的计数值，如果所有牌都发完后，你的计数值应该为零；否则就说明你计算错了。</p>
<p>An example of an unbalanced system is the KO or knockout method of card counting where the ending total is not zero. Now for the Hi-Lo blackjack system, you are trying to wait for a high positive number before betting big. This means many small cards have been used up and your edge increases when more big cards are left in the game. Also, card counting also tells you when not to bet. When there is a large negative count, then there are a bunch of small cards left in the deck and it&#8217;s best to conserve your bet and wait for this bad swing to pass.</p>
<p>还有另一类的算牌法，是“非平衡”的，比如KO算牌法，结束的时候就不是零。对于Hi-Lo算牌法来说，当你的计数值足够大时，就可以相应的提高你的下注额。因为足够大的计数值说明有许多小点数的牌已经出现了，剩余了大量的花牌，这就相应地减少了庄家优势，提升了你的胜率。相反的，当计数值是负数，且足够小的时候，你就应该停止下注了，知道计数值又回到正数。</p>
<p>We all know the casino always has the edge in blackjack, so if you complement the hi-lo card counting system to the basic strategy, you will get the maximum edge and actually eliminate the house edge and even give yourself an edge. Casinos make their profit due to this edge, meaning if you were to gain an edge, it is guaranteed to make you money in the long run. This is how these great card counters broke the bank.</p>
<p>我们知道，黑杰克游戏是有庄家优势的。但如果将Hi-Lo算牌法和基本策略卡结合起来用，这会提升你的胜率，减少庄家优势，甚至使得你的胜率超过庄家的。娱乐场就是靠这些庄家优势获利的，也就是说，只要你的胜率超过庄家的，那么你就可以反过来获利（从概率来说的确如此）。所有的算牌法都是基于这一点的。</p>
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</ul><h3>Recent Comments</h3><ul><li><a class="commentor" href="" >笨笨</a> : <a class="comment_content" href="http://www.jiandanying.com/archives/891#comment-783" title="View the entire comment by 笨笨" >呵呵，偶尔娱乐一下啦，可能那天运气在</a></li>
<li><a class="commentor" href="" >酱油</a> : <a class="comment_content" href="http://www.jiandanying.com/archives/891#comment-757" title="View the entire comment by 酱油" >75% 是你运气好，不是因为算牌。 算牌只会带来平均0.5-1%的优势。 千万不要想着你每次去都会有...</a></li>
<li><a class="commentor" href="http://www.jiandanying.com" >站长</a> : <a class="comment_content" href="http://www.jiandanying.com/archives/891#comment-726" title="View the entire comment by 站长" >很棒的成绩！</a></li>
<li><a class="commentor" href="" >笨笨</a> : <a class="comment_content" href="http://www.jiandanying.com/archives/891#comment-724" title="View the entire comment by 笨笨" >呵呵，偶最近实践的结果７５％的胜算，有一次状态很好，连续８／９叫到２１点，整桌子的人都傻眼了，我用５...</a></li>
<li><a class="commentor" href="" >gd123</a> : <a class="comment_content" href="http://www.jiandanying.com/archives/891#comment-591" title="View the entire comment by gd123" >21点光会算还是远远不够
评估一个赌戏值不值的玩

除了具体规则庄家优势外
还要看切牌的具体...</a></li>
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		<title>算牌法巡讲：Canfield-II算牌法</title>
		<link>http://www.jiandanying.com/archives/888</link>
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		<pubDate>Fri, 12 Mar 2010 13:27:16 +0000</pubDate>
		<dc:creator>站长</dc:creator>
				<category><![CDATA[21点算法|分析]]></category>
		<category><![CDATA[算牌方法]]></category>
		<category><![CDATA[翻译]]></category>

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		<description><![CDATA[The Canfield Master Count system is the harder version of the Canfield Expert system. This one is a multi-level card counting system set at Level 2 and is also classified as advanced. This level II system means that the indexes range through a greater number of values such as (-2,-1,0,+1,+2). Because of this, it is obviously much harder to learn and is more complicated because players need to memorize a greater index. Although, the difficulty is still intermediate because this is a balanced system, which means when you start the count at zero on a freshly shuffled deck, your count should also be zero at the end of the deck after all the cards have been dealt. This makes it easier to learn since you can know for sure if your count is accurate after going through a whole deck.

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			<content:encoded><![CDATA[<p>The Canfield Master Count system is the harder version of the Canfield Expert system. This one is a multi-level card counting system set at Level 2 and is also classified as advanced. This level II system means that the indexes range through a greater number of values such as (-2,-1,0,+1,+2). Because of this, it is obviously much harder to learn and is more complicated because players need to memorize a greater index. Although, the difficulty is still intermediate because this is a balanced system, which means when you start the count at zero on a freshly shuffled deck, your count should also be zero at the end of the deck after all the cards have been dealt. This makes it easier to learn since you can know for sure if your count is accurate after going through a whole deck.</p>
<p>Canfield-II算法比<a href="http://www.jiandanying.com/archives/882">Canfield-I</a>难，属于中级算法。中级算法意味着将使用到更多的计算值，比如-2、-1、0、+1、+2，因此也更难学习掌握。不过，这还不是最难的，毕竟这还是一种“平衡”算法（由零开始、到零结束）。</p>
<p>The Canfield Master actually has the same efficiency as the Expert methods but it does have a much higher betting and insurance correlation percentage【这句不明白】. This is one of the big benefits of using a more advanced count but you need to sacrifice ease for better odds and more advantage over the house. Just like the Expert style, the Master count was invented by Richard Canfield, a former pit boss who worked at casinos and wrote the book “Blackjack Your Way to Riches”. Canfield Master Count is what actually lead up to the Bryce Carlson&#8217;s Omega II count system where the indices of both systems are virtually identical.</p>
<p>高级算法学习起来比较难，但它可以帮助你获得更好的的赔率以及提高你对庄家的优势。和<a href="http://www.jiandanying.com/archives/882">Canfield-I</a>算法一样，Canfield-II算法也是有Richard Canfield——曾经是某个娱乐场的现场经理，也是“Blackjack Your Way to Riches”一书的作者——发明的。Canfield-II算法后来由Bryce Carlson改进为Omega-II算法，你会发现，这两种算法的计数值表几乎完全一样。</p>
<p>Canfield originally designed this system for single deck blackjack in the 1970s but as time went on and casinos cracked down on card counters, a one deck hand dealt game is very rare to come by. You will find many 6:5 blackjack odds tables with single decks but the 6:5 odds are a scam and i t&#8217;s just not worth playing since multiple deck 3:2 games will offer better odds with card counting anyways. The Master count lost popularity as more decks were increased to the shoe but it is still powerful if you can find a single deck game or even two decks.</p>
<p>Canfiled算法是在1970年发明这种算法的，当时是用于一副牌的，而现在几乎已经没有地方是使用一副牌的了。<em>也许你会找到一副牌的娱乐场，不过玩家黑杰克的赔率是6赔5。但我要告诉你的是，绝对不要去玩这种游戏，因为在多幅牌（玩家黑杰克3赔2）中，使用了算牌方法，可以获得比单副牌（6:5）更高的获胜率。</em>随着牌盒中牌副数的增多，Canfield-II算法也逐步退出舞台了；不过，如果你现在还能找到一副牌或两副牌的游戏，使用这种算法还是很有效果的。</p>
<p>The indexes are displayed in the table below in chart format. When viewing the left column, this shows what value of cards in the deck while the right side of the chart shows the index or distribution of count values assigned to each card.</p>
<p>这是Canfield-II算法的计数值分配表：</p>
<div>
<table cellspacing="0">
<tbody>
<tr>
<th title="This is what value card is dealt or seen on the table from either the dealer, the other players at the table or you.">牌面</th>
<th title="For every card seen on the blackjack table, add this number to your overall count value.">计数值</th>
</tr>
<tr>
<td>2</td>
<td>0</td>
</tr>
<tr>
<td>3</td>
<td>+1</td>
</tr>
<tr>
<td>4</td>
<td>+2</td>
</tr>
<tr>
<td>5</td>
<td>+2</td>
</tr>
<tr>
<td>6</td>
<td>+2</td>
</tr>
<tr>
<td>7</td>
<td>+1</td>
</tr>
<tr>
<td>8</td>
<td>0</td>
</tr>
<tr>
<td>9</td>
<td>-1</td>
</tr>
<tr>
<td>10</td>
<td>-2</td>
</tr>
<tr>
<td>J</td>
<td>-2</td>
</tr>
<tr>
<td>Q</td>
<td>-2</td>
</tr>
<tr>
<td>K</td>
<td>-2</td>
</tr>
<tr>
<td>A</td>
<td>0</td>
</tr>
</tbody>
</table>
</div>
<p>The goal is to watch the cards that are dealt to all players and to the dealer. Then you need to add up the count numbers in your indexes. For example, if two jacks and two kings are dealt in a hand, your running count would be -8. The main strategy and method with all counting systems is to bet high when the count is high, which correlates to more high valued cards such as tens in the deck, which benefits you more than the dealer in terms of probability odds and advantage edge. Likewise, when your count is low or negative, you will know when to tame your betting down a notch.</p>
<p>举个例子，如果桌面上出现了2张J和2张K，那么你的计数值应该减去8（J和K的计数值都是-2）。当你的计数值足够高的时候，比如10以上，那么就应该增加你的下注额；反之，则应该减少或者不下注。</p>
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		<title>算牌法巡讲：Canfield-I算牌法</title>
		<link>http://www.jiandanying.com/archives/882</link>
		<comments>http://www.jiandanying.com/archives/882#comments</comments>
		<pubDate>Mon, 08 Mar 2010 07:47:30 +0000</pubDate>
		<dc:creator>站长</dc:creator>
				<category><![CDATA[21点算法|分析]]></category>
		<category><![CDATA[算牌方法]]></category>
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		<description><![CDATA[There are two Canfield card counting systems out there, the Canfield Expert and Canfield Master Count. The one described on this page is the expert system. The expert count is the easier of the two to learn. It is a level 1 (single-level or level-one) strategy used for counting cards. This one is also a fairly decent one to use while playing blackjack in terms of playing efficiency.

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			<content:encoded><![CDATA[<p>There are two Canfield card counting systems out there, the Canfield Expert and Canfield Master Count. The one described on this page is the expert system. The expert count is the easier of the two to learn. It is a level 1 (single-level or level-one) strategy used for counting cards. This one is also a fairly decent one to use while playing blackjack in terms of playing efficiency.</p>
<p>一共有两种以Canfield命名的算牌法，Canfield-I和<a href="http://www.jiandanying.com/archives/888">Canfield-II</a>，也称为Canfield Expert和<a href="http://www.jiandanying.com/archives/888">Canfield Mastere</a>。这里介绍的是Canfield-I (Canfiled Expert)，是这两种算法中比较容易学习的，属于初级算法，这也是最常见的算法之一。</p>
<p>As a matter of fact, the Canfield Expert count was made popular in a book called “Blackjack Your Way to Riches”, written by none other than Richard Canfield himself. The book itself was published in 1977 so it is one of the older strategies used by counters. If you are a beginner or if you are just looking for an easy system to learn, then this one is ideal. It is balanced, which means you can start your count at zero on a new deck and when the deck is completely dealt out, your count should also be zero. This is an excellent way to know how accurate your count is and if you have been doing it correctly.</p>
<p>事实上，是《Blackjack Your Way to Riches》这本书使得Canfield-I算法流行开来的，而这本书的作者，正式 Richard Canfiled 本人。这本书是1977年第一次发行的，所以这种算法算得上比较“古老”的那种了。但如果你是算牌初学者，或者只是想找一种简单的算牌方法，那么选择这个算法牌还是不错的。另外，这也是“平衡”算法牌，也就是说，一副牌开始的时候，这种算牌法的初始值是零，而当所有牌都发完后，你的算牌结果也应该回到零；这也是很好的检验你准确率的方法。</p>
<p>For some comparison, the Hi-Opt 1 Count is just a little bit better in terms of strength and with the odds. The only drawback to the Canfield expert card count is the fact that it was designed to be used while playing single deck blackjack, which is a game that is hard to come by unless you get caught up in the 6:5 blackjack scam. Richard, the inventor of this system, was once a pit boss who worked at a casino and also worked on newsletters with Bob Gates. He is now retired.</p>
<p>看起来Canfield-I 和另一种著名的算法——Hi-Opt-I算法——比较像，但要特别指出的是：Canfield-I是专门用于一副牌BlackJack的。</p>
<p>The indexes for the Canfield Expert can be found below. The list on the left side of the chart is the card value and the other list on the table is what count value that is assigned to each card.</p>
<p>这是Canfield-I算法的计数值分配表：</p>
<div>
<table cellspacing="0">
<tbody>
<tr>
<th title="This is what value card is dealt or seen on the table from either the dealer, the other players at the table or you.">牌面</th>
<th title="For every card seen on the blackjack table, add this number to your overall count value.">计数值</th>
</tr>
<tr>
<td>2</td>
<td>0</td>
</tr>
<tr>
<td>3</td>
<td>+1</td>
</tr>
<tr>
<td>4</td>
<td>+1</td>
</tr>
<tr>
<td>5</td>
<td>+1</td>
</tr>
<tr>
<td>6</td>
<td>+1</td>
</tr>
<tr>
<td>7</td>
<td>+1</td>
</tr>
<tr>
<td>8</td>
<td>0</td>
</tr>
<tr>
<td>9</td>
<td>-1</td>
</tr>
<tr>
<td>10</td>
<td>-1</td>
</tr>
<tr>
<td>J</td>
<td>-1</td>
</tr>
<tr>
<td>Q</td>
<td>-1</td>
</tr>
<tr>
<td>K</td>
<td>-1</td>
</tr>
<tr>
<td>A</td>
<td>0</td>
</tr>
</tbody>
</table>
</div>
<p>Notice that the aces count as 0. This means that the Canfield expert is not Ace-reckoned, meaning you may need to count the aces on the side in order to improve the efficiency of your odds and strategy. On a good note, you do not need to be aware of the suits on each card, which can make the count more complicated.</p>
<p>注意，在这里Ace的计数值是零，也就是说，Canfield-I是不统计Ace的。这也意味着，你最好另外记录一下Ace出现的次数，这应该会额外提高你的胜率。另外，这种算法不需要区分牌的花色，这会使得你的算牌更加简单。</p>
<p>Since this is a level I system, you only need to pay attention to just three numbers for the indices (-1,0,+1), making it an easy one to learn when you are just starting out. Now the goal is to watch the cards and keep track of the count. For example, when low cards are dealt, you start adding +1 to your running mental count and when the high cards are dealt, you subtract (-1) to your total count. The idea is to bet high when the count is high and positive and bet low when the count is low or negative. The high count corresponds to large card values such as 10s and 9s. These will benefit the player more than the dealer in terms of mathematical odds.</p>
<p>这只是初级算牌法，你只要使用三种计数值（-1、0、+1），这应该很容易学习上手。当小点数牌出来的时候，你应该快速地将心中的计数结果+1，而当大点数牌出现的时候就应该是-1。而当计数结果足够高（比如9或者10以上）的时候，你就应该提高你的下注额；相对的，就应该降低注额，或者不下注。因为如此高的计数结果，意味着玩家比庄家拥有更大的获胜优势。</p>
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</ul><h3>Recent Comments</h3><ul><li><a class="commentor" href="http://www.jiandanying.com" >站长</a> : <a class="comment_content" href="http://www.jiandanying.com/archives/882#comment-178" title="View the entire comment by 站长" >之后几天，我会发一些算法的翻译稿，大概有十几篇。</a></li>
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