简单赢：赢，就是简单！ » 21点算法|分析

算牌法巡讲：KISS-II算法

站长 — Tue, 18 May 2010 02:50:19 +0000

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.

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。

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.

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KISS-III算牌法，以获得更好的效果。

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.

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。

牌面	计数值
2	0/+1
3	+1
4	+1
5	+1
6	+1
7	0
8	0
9	0
10	-1
J	-1
Q	-1
K	-1
A	0

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.

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。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。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%。

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.

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。

算牌法巡讲：KO算法

站长 — Mon, 10 May 2010 06:43:53 +0000

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.

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Hi-Lo算牌法、HiOpt-I算牌法、HiOpt-II算法牌等等，所有这些算牌法的基本概念都是：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）。

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’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.

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”）。KO算牌法就是一种非平衡算牌法。

KO Card Counting Strategy

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.

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。

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.

牌面	计数值
2,3,4,5,6,7	+1
8,9	0
10,J,Q,K,A	-1

Benefits of KO Card Counting

KO算牌法的优势

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’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.

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。

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.

（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。

The benefit of this system is you don’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’t much different between the Hi-Lo card system and the KO counting system either.

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Hi-Lo算牌法的区别并不大。

算牌法巡讲：HiOpt-II算法

站长 — Sat, 01 May 2010 09:41:56 +0000

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.

HiOpt-II是另一种常被高级玩家使用的算牌方法，是HiOpt-I算牌法的第二个版本。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。

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’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.

建议：在学习HiOpt-II算牌法前，先练习掌握Hi-Lo算牌法或KO算牌法。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。

Difference between Hi-Opt II and Hi-Opt I

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’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.

HiOpt-II和HiOpt-I算牌法的区别

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HiOpt-I算牌法更难掌握。还有一个区别就是，在HiOpt-II中要记录2和7这两个原本在HiOpt-I算牌法中不需要记录的牌。但同样的，这两种算牌法都是“平衡”算牌法。

Hi-Opt II Card Counting Strategy

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.

之前在《算牌法巡讲：HiOpt-I算法》中曾说过，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。

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’s cards on the table in order to get a good prediction of what cards are still left in the deck.

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。

牌面	计数值
2	+1
3	+1
4	+2
5	+2
6	+1
7	+1
8	0
9	0
10	-2
J	-2
Q	-2
K	-2
A	0

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.

When to Bet in Hi-Opt II Card Counting

关于HiOpt-II算牌法的下注时机

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.

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。其实，算牌法就是告诉你“好运气”是否来到了。

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.

要特别提醒你的是，要用“真数”来作为你的决策依据。所谓真数，就是将计数值除以剩余的牌副数得到的数值。比如，计数值是+4，剩余4副牌，那么此时的真数就是+1了。

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.

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。

算牌法巡讲：HiOpt-I算法

站长 — Tue, 20 Apr 2010 03:48:45 +0000

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.

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Hi-Lo算牌法很相似，而且也是“平衡”算牌法（由零开始，到零结束）。

Because of this system’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.

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Hi-Lo算牌法再来学HiOpt-I算牌法。

Hi-Opt I Card Counting Strategy Guide

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.

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。

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’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:

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：

牌面	计数值
2	0
3	+1
4	+1
5	+1
6	+1
7	0
8	0
9	0
10	-1
J	-1
Q	-1
K	-1
A	0

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’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’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’t care.

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。
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。

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’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 slight change to the basic strategy because of this.

……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。

牌桌上的坏策略 Bad Strategies

站长 — Sat, 10 Apr 2010 09:49:56 +0000

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%.

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%。

Never bust: 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%.

永不爆牌：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%。

Mimic the dealer: 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%.

模仿庄家：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%。

Assume a ten in the hole: 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%.

假设庄家的底牌是10：……这种策略下，庄家优势将提高到10.03%。

算牌法巡讲：Hi-Lo / High Low算牌法

站长 — Fri, 19 Mar 2010 07:49:51 +0000

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.

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。

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:

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。

牌面	计数值
2,3,4,5,6	+1
7,8,9	0
10,J,Q,K,A	-1

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!

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。

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’s best to conserve your bet and wait for this bad swing to pass.

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。

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.

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。

算牌法巡讲：Canfield-II算牌法

站长 — Fri, 12 Mar 2010 13:27:16 +0000

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.

Canfield-II算法比Canfield-I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）。

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’s Omega II count system where the indices of both systems are virtually identical.

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Canfield-I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。

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’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.

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。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。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。

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.

这是Canfield-II算法的计数值分配表：

牌面	计数值
2	0
3	+1
4	+2
5	+2
6	+2
7	+1
8	0
9	-1
10	-2
J	-2
Q	-2
K	-2
A	0

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.

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。

算牌法巡讲：Canfield-I算牌法

站长 — Mon, 08 Mar 2010 07:47:30 +0000

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.

一共有两种以Canfield命名的算牌法，Canfield-I和Canfield-II，也称为Canfield Expert和Canfield Mastere。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。

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.

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。

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.

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。

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.

这是Canfield-I算法的计数值分配表：

牌面	计数值
2	0
3	+1
4	+1
5	+1
6	+1
7	+1
8	0
9	-1
10	-1
J	-1
Q	-1
K	-1
A	0

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.

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。

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.

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。

探讨一下分牌

站长 — Thu, 07 Jan 2010 09:55:00 +0000

上次发了双倍下注的数学依据和分Ace的数学依据，这次轮到分牌的数学依据了。

除了A-A分牌的情况外，其它对子的分牌是还可以继续拿牌的。A-A分牌已经在之前的文章中专门说过了，这里就只讨论除此以外的对子分牌情况。

其实考量的标准很简单：是否增加了胜率？

=================我是分隔线，上下的文字相差了差不多2周的时间===================

原本以为这个话题会比较简单，没想到事实上很复杂，比想象中复杂地多。

要比较“胜率的变化”，当然要计算出分牌后的新胜率，而这个“新胜率”就是问题所在。因为不同于分A，普通的分牌是允许继续要牌、甚至双倍加注的，所以这个新胜率就相当于要算出任1张牌在当前规则下的最终点数分布。

先说简单的情况，拿牌。就不是类似庄家的拿牌，死拿到17点才罢手，而是只有拿牌胜率大于停牌胜率的时候才拿牌。

然后复杂点，分牌。相当于又开始了一个新的单张牌计算最终点数分布的过程。

最后，双倍加注。如果双倍加注的机会出现了，当然要双倍加注（原因我会在下一篇讨论的），所以在允许双倍加注的时候，还要多计入这个因素。

而且，以上的这些设计的分牌规则、双倍加注规则在不同的娱乐场又有差异，这些都要作为“桌面规则”考虑进去。

呵呵，所以就花了我这2周的时间，来搞定这些。

呼呼，这就是理科生的乐趣所在：头疼——>折磨——>豁然开朗——>搞定！

标准规则下，庄家最终点数的预期分布

站长 — Fri, 25 Dec 2009 13:14:57 +0000

用算牌器可以很容易地算出在各种规则下，庄家最终点数的预期分布，这里先公布标准规则下的。

标准规则是这样的：

8副牌；
自动循环洗牌；
庄家16点以下必须拿牌，17点以上必须停牌；
玩家黑杰克获胜的赔率为2赔3。

在这个规则下，庄家最终点数的预期分布为：

17点：14.5%；
18点：14.0%；
19点：13.4%；
20点：18.0%；
21点：7.30%;
黑杰克：4.7%；
爆牌：28.1%。

分Ace的数学依据

站长 — Fri, 18 Dec 2009 03:01:08 +0000

上次发了双倍下注的数学依据，这次接着来，这次来分析一下为什么所有的策略都说“玩家两张A的时候，除非庄家也是A，否则都选择分牌”？而我们知道，A-A分牌后是必须停牌的，那么，这个策略的数学依据是什么呢？

我们首先来看对照面，即A-A不分牌的情况，假设玩家也执行庄家的规则，即“16点及以下要牌，17点（包括软17）及以上停牌”。那么，在这种情况下，玩家的点数预期分布为：24.5%会爆牌，拿到17到21的概率都是15.1。

再来看看A-A分牌，面对庄家不同明牌的胜率期望（如果有计牌器就一目了然了）：

庄家明牌2：玩家分牌胜率是65.8%；
庄家明牌3：玩家分牌胜率是66.8%；
庄家明牌4：玩家分牌胜率是68.0%；
庄家明牌5：玩家分牌胜率是69.1%；
庄家明牌6：玩家分牌胜率是70.2%；
庄家明牌7：玩家分牌胜率是65.3%；
庄家明牌8：玩家分牌胜率是62.5%；
庄家明牌9：玩家分牌胜率是59.4%；
庄家明牌是10-K的花牌：玩家分牌胜率是53.6%；
庄家明牌A：玩家分牌胜率是39.4%。

可见，只要庄家的明牌不是A，玩家A-A分牌后，都有超过50%以上的胜率。这个数值，远远好于不分牌的情况。

这个很能说明问题

站长 — Thu, 17 Dec 2009 13:31:55 +0000

下图也是打完一整盒牌后我的计牌器的截图：

我打了一开始的三局牌，很幸运的全胜。从第四局开始，计牌器的指标就显示优势偏向庄家了，然后我就没有下注。没想到从那一局开始，指标就一直没有扭转回来，我也就一直没有下注参加，只是记录了每一局牌，直到这一盒结束。

从这张图就可以看出，全桌一共玩了64手牌，其中庄家净胜19手。净胜是指胜负相抵后的结果，这相当于庄家在这全部64手牌中，胜41手、负22手、平1手，多么离谱的胜率呀。

这也同时证明了，这些指标还是挺有用的。

双倍下注的数学依据

站长 — Mon, 07 Dec 2009 07:57:26 +0000

举一个例子，假设庄家明牌是6，玩家拿到了9-2，所有的策略卡都会给出“双倍下注”的建议。我们现在来通过简单的概率计算，算一下此时双倍下注的数学依据在哪里。

因为双倍下注只能拿一张牌，也就是说，这是个是否要押注买这一张牌的问题。

这种1张定胜负的游戏，只要看胜率就可以，胜率大于50%，就押注；小于50%，则当然不押。

如果这时候你有算牌器，就很容易计算拿牌的胜率了；如果没有，就按照基本策略卡执行就是了。

具体到我自己，我会对双倍下注再多2个条件：
1、拿牌胜率要60%以上，而不是仅仅50%；
2、拿牌胜率要大于停牌胜率。

关于1，比如玩家11对庄家明牌10，基本策略卡是要求双倍下注。但这个时候，双倍的胜率只有53%，并不是一个很高的胜率。

关于2，比如玩家A-7对庄家明牌6，基本策略卡是要求“双倍，如果不能双倍就停牌”。但这个时候，停牌的胜率是69%，双倍的胜率是63%，也就是说，降低了胜率。这种情况下的双倍，不见得是一个好的决策。

下次有机会我们再来分析一下《分牌的数学依据》。

《决胜21点》中的三门问题

站长 — Fri, 27 Nov 2009 03:35:25 +0000

题目是这样的：“在你面前有三扇门，只有一扇门后有轿车、另两扇门后是羊。先让你选择一扇门，然后主持人去门后观察，在另两扇门中打开一扇是羊的门。这时你有更换选择的权利，请问你换不换最初的选择？”

片中给出的答案是换，可以将胜率从33%提高到66%。可仍然有许多人对此怀疑，我试着用简单的方法来解释一下这个答案是怎么来的。

方法一，枚举。

1、初始状态共有三种：CSS、SCS、SSC。可知这三种是同概率的，故只要枚举其中的一种即可，如CSS。

2、先枚举换的情况，我们将门从左到右标记为1号门、2号门、3号门。
2.1、选择1号门，开2号门，换，失败；这种情况的概率为1/3×1/2=1/6；
2.2、选择1号门，开3号门，换，失败；这种情况的概率为1/3×1/2=1/6；
2.3、选择2号门，开3号门，换，成功；这种情况的概率为1/3；
2.4、选择3号门，开2号门，换，成功；这种情况的概率为1/3。
即，更换选择这种策略的胜率为1/3+1/3=2/3=66%。

3、再枚举不更换的情况：
3.1、选择1号门，开2号门，不换，开3号门，成功；这种情况的概率是1/3×1/2=1/6；
3.2、选择1号门，开3号门，不换，开2号门，成功；这种情况的概率是1/3×1/2=1/6；
3.3、选择2号门，开3号门，不换，开1号门，失败；这种情况的概率是1/3；
3.4、选择3号门，开2号门，不换，开1号门，失败；这种情况的概率是1/3。
即，不更换选择这种策略的胜率为1/6+1/6=1/3=33%。

方法二，还有更简单的理解方法，但读起来挺拗口的。
1、不更换的情况，胜率是1/3，这一点我想不会有人有疑问。
2、在这个游戏设定中的更换，只有2种结果，“车换成羊”和“羊换成车”，不存在“羊换成羊”的情况。也就是说，是“胜换成败”和“败换成胜”；也就相当对调了“不更换”情况下的的胜败结果，将1/3的胜率变成了1/3的败率，2/3的败率变成了2/3的胜率。

21点技巧——算牌法

站长 — Tue, 10 Nov 2009 02:38:00 +0000

像轮盘这类娱乐游戏，每次轮盘转出什么结果，和上一次完全没有关系。还有牌九这类游戏，每玩过一轮，就重新洗牌。这些游戏里，每一手都是互相独立的。而二十一点则不同，前一把出现了什么牌，会直接影响到下一把。因此，如果我们能记住前面出过什么牌，就能大致预测以后的赌局走势，从而调整自己的赌注，在对自己有利时下大注，在对庄家有利时下小注或不下注，从而占到优势。

二十一点算牌法最早出现在六十年代初。1962年《打败庄家（Beat the Dealer）》一书问世，向公众系统介绍了算牌法。这不再是我们惯见的萝卜赌经，而是有数学基础的方法，因为它在不同的赢牌概率Pi时下不同的赌注B(i)，虽然总的胜利概率之和ΣP(i)仍然小于1/2，但只要在P(i)大时下大的B(i)，P(i)小时下小的B(i)，就能使总回报ΣR(i)P(i)大于ΣB(i)。

“算10法”比较难操作，需要极高的心智和注意力。不过经过无数玩家的不懈探索，算牌方法不断到进化，越来越简单实用。现在比较流行的一种叫“高低法（High-Low）”。在游戏过程中，我们把每一张出现的2，3，4，5，6都算＋1点，7，8，9算0点，10，J，Q，K，A算－1点，将各点相加，结果越大，就表示前面出现过的小牌越多，对玩家越有利。反过来，如果结果是个负数，就表示前面出过的大牌比小牌多，对庄家有利。比如前面出现的牌是：
4，9，10，5，J，A，8，10，Q，2，6，K，J，7
那么点数就是4张小牌减7张大牌，是－3。当然，在游戏过程中，你不可能叫庄家把牌局暂停，让你从容加减。你必须在每张牌出来时，就在心里默算点数。从第一张牌出现开始，你就应该在心里默算出：
1，1，0，1，0，－1，0，－2，－3，－2，－1，－2，－3，－3
在实际运用中，还可以采取两张牌一计的技巧，因为庄家发牌时一般速度较快，这样可以方便地把很多同时出现的大牌和小牌抵消不计，提高了算牌速度，减少了可能的计算错误。比如在上面的例子里，如果两张牌一计，那就是：
1，1，－1，－2，－2，－2，－3

如果是一副牌，－3已经是很糟糕的点数了，这时应该下最小注，或者停止不玩。不过一般来说，现在的赌场都使用六到八副牌，那么在六副牌312张牌内，发出14张牌，还剩298张牌，平均每副牌的点数是（－3）×52/298＝－0.5，还算可以忍受。
在点数变大时，该怎么提高赌注，每个算牌手都有自己的习惯和算法。理论上，如果你占A的优势，本钱总数为R，那么最优赌注是B=A×R。

比如你有一万块钱的本钱，现在你占1%的优势，那么就应该在这把压下一百块钱。虽然理论上此法可以获得最大回报，但在实践中过于冒险，只可视为下注时的上限。

在点数为0或负数时，玩家应当下最小赌注。当然，最好是干脆不玩，坐等点数变正。早期的那些算牌手就是这么做的，现在的赌场里，从游弋在各桌间的桌面经理，到高悬在天花板上的监视器，都虎视耽耽地监视着每个玩家的行为。如果总是点坏不压、点好猛压，还不如直接在脸上写五个大字：“我是算牌手”，说不定还暴露得晚些。这也是在线 21点游戏的一大优势，没有了背后咄咄的目光，更从容的使用所有的基本策略和算牌法，从而最大限度的削弱在线赌场的优势，赢取赌金，现在就开始你的在线21点之旅吧。

21点算法

站长 — Mon, 09 Nov 2009 10:01:30 +0000

二十一点能够算牌，是因为我们在讨论“基本策略”时提出的一个假设不成立：

假设52张牌出现的概率始终相同，也就是说每张牌都是从一个无穷多副牌组成的牌盒里抽出来的，或者说前面出过的牌不影响后面的牌，换句话说，每张牌相互之间都是独立的。

显然，不可能有这样的由无穷多副牌组成的牌盒，前面出过的牌总会影响后面的牌。在算牌法刚出现的时代，赌场仍然使用一副牌来玩二十一点，那么这个影响就更明显。比如，发牌员发出牌来，你拿到两个10（包括J、Q、K），庄家亮牌也是10，翻出底牌来还是10，那么下一轮里10出现的概率已不再是4/13，而是12/48，即1/4，略低于4/13。同样的，其他点数出现的概率也已不再是1/13，而是1/12。

象轮盘赌这类游戏，每次轮盘转出什么结果，和上一次完全没有关系。还有牌九这类游戏，每玩过一轮，就重新洗牌。这些游戏里，每把赌博之间都是互相独立的。而二十一点的各把之间，在重新洗牌之前，不是独立的。前一把出现了什么牌，会影响到下一把。因此，如果我们能记住前面出过什么牌，就能大致预测以后的赌局走势，从而调整自己的赌注，在对自己有利时下大注，在对庄家有利时下小注或不下注，就能在这个游戏里占到优势。

UCLA的数学教授爱德华·索普（EdwardThorp）在六十年代初发明了二十一点算牌法。他注意到，如果二十一点里10出现的概率增高，对庄家是不利的，因为庄家在十六点及更低时必须要牌，10越多，就越容易爆掉，而对玩家来说，则更容易拿到BJ，赢一倍半的钱。所以他用一种“算10法（10-Count）”，计算剩下的牌中10的比例。正常情况下，这个比例应该是4/13，庄家占优势。但当前面出掉很多小牌，10的比例达到1/3时，优势就转移到玩家这边来了。

索普的运气不错，那时计算机也发明出来了，他找到IBM公司里的朋友，写了个程序来验证自己的算牌方法。那时的计算机跟今天比起来，还是速度低下、体积庞大的蠢物，足足运转了七天七夜，终于证明了这个方法是可行的。索普又自己到赌场里亲自实践，结果果然大赢特赢。

1962年他出版了《打败庄家（BeattheDealer）》一书，向公众介绍了自己的算牌法。这不再是我们惯见的萝卜赌经，而是有数学基础的方法，因为它在不同的赢牌概率P（i）时下不同的赌注B(i），虽然总的胜利概率之和ΣP（i）仍然小于1/2，但只要在P（i)大时下大的B(i)，P(i)小时下小的B（i），就能使总回报ΣR（i）P（i）大于ΣB（i）。

“算10法”比较难操作，需要极高的心智和注意力。好在群众的智慧是无穷的，算牌手们沿着索普指定的方向走下去，已经把算牌方法演进得越来越简单实用（索普本人在60年代后期就淡出了赌博界，带着他在赌场赢来的大笔资金，进入股票市场，运用他的数学知识，现在已成为超级巨富）。

我使用的是一种叫“高低法（High-Low）”的算牌法。在游戏过程中，我们把每一张出现的2，3，4，5，6都算＋1点，7，8，9算0点，10，J，Q，K，A算－1点，将各点相加，结果越大，就表示前面出现过的小牌越多，对玩家越有利。反过来，如果结果是个负数，就表示前面出过的大牌比小牌多，对庄家有利。

比如前面出现的牌是：

4，9，10，5，J，A，8，10，Q，2，6，K，J，7

那么点数就是4张小牌减7张大牌，是－3。当然，在游戏过程中，你不可能叫庄家把牌局暂停，让你从容加减。你必须在每张牌出来时，就在心里默算点数。比如在上面的例子里，从第一张牌出现开始，你就应该在心里默算出：

1，1，0，1，0，－1，0，－2，－3，－2，－1，－2，－3，－3

在实际运用中，还可以采取两张牌一计的技巧，因为庄家发牌时一般速度较快，这样可以方便地把很多同时出现的大牌和小牌抵消不计，提高了算牌速度，减少了可能的计算错误。比如在上面的例子里，如果两张牌一计，那就是：

1，1，－1，－2，－2，－2，－3

如果是一副牌，－3已经是很糟糕的点数了，这时应该下最小注，或者停止不玩。不过一般来说，现在的赌场都使用六到八副牌，那么在六副牌312张牌内，发出14张牌，还剩298张牌，平均每副牌的点数是（－3）×52/298＝－0.5，还算可以忍受。

显然，在每一盒牌（“盒（shoe）”是指一盒牌从开始发牌到洗牌的过程，这一盒牌里可能有六副、四副、八副或其他副数的牌）的开始，由于大部分牌还未发出，因此平均点数总是在0左右。要到牌盒里剩下的牌不多时，平均点数才可能比较显著地偏离0。所以算牌手在算牌时都会寻找合适的赌桌，一方面要找人少的桌子，因为人越少，你在单位时间内玩的次数越多，实际收益才会更逼近期望值；另一方面要找切牌少的发牌员，因为该切多少牌，赌场只有个大概的规定，具体执行还是要靠发牌员的觉悟，所以同一家赌场里，不同的发牌员切出的牌来常会差很多。

在点数变大时，该怎么提高赌注，每个算牌手都有自己的习惯和算度。贝尔实验室的J.L.Kelly推导出，在理论上，如果你占A的优势，本钱总数为R，那么最优赌注是B=A*R。

比如你有一万块钱的本钱，现在你占1%的优势，那么就应该在这把压下一百块钱。这种下注法称为Kelly法，是在理论上可以获得最大回报的方法。但在实践中，Kelly法过于冒险，只可视为下注时的上限。

斯坦福·王（StanfordWong）在《二十一点的秘密(BlackjackSecrets）》里说，平均点数每高一点，可增加约0.5％的优势。他是二十一点算牌界里最有名的祖师爷级人物之一，甚至排在爱德华·索普之前，第一个进入了“二十一点名人堂（BlackjackHallofFame）”。我第一次看到他的名字时，还以为他是个华裔，后来在电视上看到他，才发现他是个白人老头。斯坦福·王其实是他的艺名：他毕业于斯坦福大学，再加上“王”这个很有气势的东方姓氏。他对中国文化好像很感兴趣，自己创办了一家出版社，就叫“PiYee”——念念看吧：什么？辟易？便宜？别数典忘祖了，人家这叫“牌艺出版社”！

按照他的说法，在0点时，庄家占0.5％的优势。到了1点，双方差不多扯平。平均点数升到2时，玩家就已经占0.5％的优势，可以提高赌注了。如果按照Kelly法，平均点数为7时，玩家占3％的优势，就得将自己全部本钱的3％投进去，显然太过冒险了。

在点数为0或负数时，玩家应当下最小赌注。当然，最好是干脆不玩，坐等点数变正。早期的那些算牌手就是这么做的，但现在的赌场里，从游弋在各桌间的桌面经理，到高悬在天花板上的监视器，都虎视耽耽地监视着每个赌徒的行为。如果总是点坏不压、点好猛压，还不如直接在脸上写五个大字：“我是算牌手”，说不定还暴露得晚些。

算牌本身并不难练，难的是和赌场的斗智斗勇。在《打败庄家》刚出版时，它轰动一时，很快成为畅销书，激励了无数赌徒涌向赌场，一试身手。赌场对此大为恐慌，有些赌场甚至关闭了二十一点赌桌。但是，很快他们就又恢复了镇定，因为他们发现，涌来的大批赌徒中，只有极少数人真正掌握了算牌法，其他大多数人只不过是一知半解、道听途说的萝卜。索普这本书为极少数人提供了打败庄家的方法，但对大多数人来说，实际效果却是个二十一点的广告，让他们自以为也能够在二十一点上赢钱。这是个赌场梦寐以求的广告，是他们自己无论花多少钱都做不来的广告。

在刚开始时，算牌还是个新鲜事物，没有这方面的法律规定，开赌场的又多是黑社会，一旦发现算牌手，一律当老千处理，痛打一顿后扔到臭水沟里。后来大家总算对算牌达成了共识：这是样技术活儿，是在遵守赌场规则的情况下，靠自己的聪明才智来赌博的一种方式；同时各大赌场也多被华尔街的金融巨头接管，开始西装领带的管理方式，摆开堂堂之阵来赚钱，于是算牌手总算不再有人身危险，但赌场既然是人家的私有财产，就有权把某些他们不欢迎的人拒之门外。因此，对一个算牌手来说，难的不是算牌，而是如何不被赌场发现。

同时，赌场也巧妙地改变了规则，比如用八副牌代替一副牌，牌发到一半时就重新洗牌，不准在一局牌的中间加入赌局等等，极大地增加了算牌的难度。他们逐渐稳住阵脚后，便大开二十一点赌桌，从此二十一点就取代了“蟹赌（Crap）”，成为赌场里最热门的游戏。但在算牌法已经发明了四十多年后的今天，我们在二十一点赌桌上见到的，仍然大多数是萝卜。

拿到了黑杰克，还需不需要买保险？

站长 — Mon, 09 Nov 2009 06:18:25 +0000

如题。如果单纯从概率的角度来计算，是很容易的。

局面，玩家黑杰克、庄家明牌A（庄家拿到黑杰克的概率为4/13），设玩家注额为1。

一、如果玩家不买保险，则玩家的预期收益为：
1、庄家没有黑杰克，玩家获赔1.5倍注额，即1.5×9/13；
2、庄家拿到黑杰克，玩家没输赢，即0×4/13；
3、合计预期收益为1.5×9/13+0×4/13=1.5×9/13=1.038。

二、如果玩家买保险，即还需要加注0.5，则玩家的预期收益为：
1、庄家没有黑杰克，玩家获赔1倍注额，即(1.5-0.5)×9/13；
2、庄家拿到黑杰克，玩家获赔1倍注额，即(1+1.5-1-0.5)×4/13；
3、即这种情况下玩家恒定获得1倍注额的赔付；
4、合计预期收益为1。

一、二比较可知，不买保险依旧比买保险多3.8%的收益。

当然，这只是单纯的概率计算，实战中，还是要审时度势来研判是否买保险。

21点(blackJack)高级算牌法(只适用一幅牌)

站长 — Fri, 06 Nov 2009 08:25:34 +0000

二十一点（BlackJack）这个是现在网络上和现实生活当中非常流行的扑克玩法。基本方法就不用介绍了，我今天主要跟大家讲的是高级算牌方法，只适用一幅牌。
Tips：一副牌的21点游戏，玩家占0.10%的优势！别小看这0.10%，这是唯一玩家占优势的娱乐场游戏。正因为如此，基本上没有什么娱乐场敢于提供，再加上算牌，庄家惨了！所以网络上的21点扑克以及赌场的扑克都是4幅牌的。

下面这种算牌方法与下注技巧适合只用一副牌的二十一点游戏

1、设定初始算牌总值为4
2、10, J, Q, K 的赋予值为 -2
3、所有其它牌的赋予值为 +1
4、开始发牌后按照发出牌所赋予的值进行加减计算出牌总值以确定如何下注，当出牌总值为负数时，下注要小，当出牌总值为正数时，下注要大
5、只有出牌总值为正数时买保险
6、玩牌过程中按照21点基本策略要牌或不要牌

1. Start the count at -4 when the deck is shuffled.
2. Count -2 for 10, J, Q, K
3. Count +1 for everything else (including aces)
4. Bet low when the count is negative, high when the count is positive.
5. Take insurance when the count is positive.
6. Play basic strategy at all times during this process.

教您辨别21点游戏中的”收先陷阱”

站长 — Fri, 06 Nov 2009 07:27:25 +0000

　　当玩家拿到 Black jack（K、Q、J、10都当10点，A可当1点或11点，首两张牌构成21点称为Black jack），而庄家的牌面为A时，庄家似乎替赌客的利益着想，问玩家要不要Even Money？澳门赌场的荷官则问：“收唔收钱先？”；对不拿 BJ的玩家则问：“要唔要买保险？”

　　玩家拿了Black jack，倘庄家不是拿Black jack，则可获（按押注的）1.5倍的彩金，但先收（Even Money），只获 1赔 1的平赔；倘玩家与玩家补牌后拿到与玩家相同的牌，则当打和，谁也没有赢输。这是牌规。

　　不少中国玩家，遇到自己拿到Black jack，而庄家的的亮牌是A 的时候，都爽快地同意荷官的建议“收先”并认为赌场这个规矩对玩家有利。

　　有人认为中国人的传统智慧“一鸟在手胜于十鸟在林”可能是促使中国赌客急于“收先”的潜意识所在。不过笔者认为，主要是由于信息不完全而导致玩家作出错误的决策。倘有人将这样的信息告知玩家；迟收一两分钟，只要庄家补来的一张牌不是10点，你就可以获得1.5倍的派彩，而庄家有的补牌有9∕13机会不是来10点的，即有约七成（9∕13＝69.23％）机会获得1.5倍赔付。或者再用收益率向玩家解释。“不早收”的期望收益率是：E（ξno）＝1.5×9∕13＝13.5∕13。

　　“先收”的收益率是：E（ξyes）＝1。

　 “先收”的期望值为：1－13.5∕13＝－0.5∕13＝－3.85％＜0。

　　也就是说，同意“先收”平均令玩家的收益减少3.85％。

简单赢：赢，就是简单！ » 21点算法|分析

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