撲克21點作弊演算法【綜合文 FreeXploiT收集整理】僅供研究,不要非法使用

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21點規則與基本玩法(中文)

玩家需將賭注置於下注圈中央。然後,莊家給每個玩家發兩張牌,牌面朝上;給自己發兩張牌,一張牌面朝上,一張牌面朝下。K、Q、J 和 10 牌都算作 10 點。 A 牌既可算作 1 點也可算作 11 點,由玩家自己決定。其餘所有 2 至 9 牌均按其原面值計算。 如果玩家拿到的前兩張牌是一張 A 和一張 10,就擁有黑傑克 (Blackjack);此時,如果莊家沒有黑傑克,玩家就能贏得 1.5 倍的賭金(2 賠 3)。沒有黑傑克的玩家可以繼續拿牌,以使總點數儘可能接近但不超過 21 點;如果超過 21 點,玩家就會“爆破”並輸掉賭金。如果莊家的總點數等於或少於 16 點,則必須拿牌;如果莊家的總點數等於或多於 17 點,則必須停牌。

二十一點術語

拿牌:(hit)

再拿一張牌。

停牌:(stay)

不再拿牌

分牌:(split)

玩家再下一注與原賭注相等的賭金,並將前兩張牌分為兩副單獨的牌。這兩張牌的點數必須相同(即一對 8、一對 K 和一對 Q)。分成兩副牌之後,一張 A 牌和一張 10 牌只能算作 21 點,不能算作黑傑克。

雙倍下注:(Double)

玩家在拿到前兩張牌之後,可以再下一注與原賭注相等的賭金(如果覺得少可以加倍),然後只能再拿一張牌。如果拿到黑傑克,則不許雙倍下注。

保險:(insurance)

如果莊家牌面朝上的牌是 A,玩家可以買保險,也就是 相當於 原賭注一半的額外賭金。如果玩家確信莊家下一張是 10 點牌,則可以買保險。如果莊家確實有黑傑克,玩家將贏得 2 倍的保險賭金;如果莊家沒有黑傑克,玩家將輸掉保險賭金,遊戲照常繼續。黑傑克要大於其他總點數為 21 點的牌。

二十一點拿牌:(hit), 停牌:(stay), 分牌:(split), 雙倍下注:(Double)基本原則(Basic Strategy)圖表:

                                          

 Dealer’s Up Card
Your
Hand
2345678910A

8

HHHHHHHHHH
9HDDDDHHHHH
10DDDDDDDDHH
11DDDDDDDDDH
12HHSSSHHHHH
13SSSSSHHHHH
14SSSSSHHHHH
15SSSSSHHHHH
16SSSSSHHHHH
17SSSSSSSSSS
A,2HHHDDHHHHH
A,3HHHDDHHHHH
A,4HHDDDHHHHH
A,5HHDDDHHHHH
A,6HDDDDHHHHH
A,7SDDDDSSHHH
A,8SSSSSSSSSS
A,9SSSSSSSSSS
A,APPPPPPPPPP
2,2HHPPPPHHHH
3,3HHPPPPHHHH
4,4HHHHHHHHHH
6,6HPPPPHHHHH
7,7PPPPPPHHHH
8,8PPPPPPPPPP
9,9PPPPPSPPSS
10,10SSSSSSSSSS

                            

說明:

1.該圖表前提是莊家軟17點不再拿牌(軟17點是指17點牌因為A的存在也可算作7點牌的情況)

2.圖表上邊一行數字是指莊家明牌點數,左邊一列是指玩家手中牌的總點數及開始兩張牌的牌型,如A,2是指開始兩張牌一張是A,一張是2;8,8是指開始兩張牌都是8

3.圖表中字母含義:H(Hit) 拿牌;  S(Stay) 停牌; P(split) 分牌; D(Double) 雙倍下注

4.應該記住,即使按照上述圖表來玩,也並不能保證你一定贏錢,只是增加贏的機會而已,總體來講,你贏的機率依然小於莊家。玩21點只有當你會算牌的時候,你贏的機會才會超過莊家,以後我們會陸續介紹21點各種算牌方法。(It needs to be noted that using the below tables will not cause you to make money – the odds are still against you. The only way to put the odds of Blackjack in you favor is to count cards which is a large topic of its own.)

二十一點高階算牌法


下面這種算牌方法與下注技巧適合只用一副牌的二十一點遊戲

1 設定初始算牌總值為4

2 10, J, Q, K 的賦予值為 -2

3 所有其它牌的賦予值為 1

4 開始發牌後按照發出牌所賦予的值進行加減計算出牌總值以確定如何下注,當出牌總值為負數時,下注要小,當出牌總值為正數時,下注要大

5 只有出牌總值為正數時買保險

6 玩牌過程中按照21點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.

一種簡單易學的二十一點算牌方法


Counting cards is the method by which players can beat the game of blackjack. Of the many excellent counting systems available, you will be learning the commonly used high-low system.

玩21點,只有會算牌,你贏的機會才會超過莊家。算牌方法有多種,在此介紹一種簡單易學的算牌方法,稱為高-低算牌法。

 
步驟
瞭解21點基本規則
 
瞭解與拉斯維加斯21點規則對應的21點玩牌基本策略(見前面文章).
 
準備一副52張撲克派,洗牌四次.
 
象正規21點賭桌一樣發牌,要牌.
 
按照每張牌設定的數值進行加減計算.
 
每張牌的數值設定如下: A,K,Q,J,10 都算 -1 (Aces and 10-value cards (kings, queens, jacks and tens) are worth -1); 2,3,4,5,6 都算 1 (twos, threes, fours, fives and sixes are worth 1); 7,8,9 都算 0 ( sevens, eights and nines are worth 0).
 
 
Tips:

算牌其實就是 1 的加減,當 1 與 -1 牌成對出現時,其和為零,如 10,6; K, 2;Q, 4;等

 
 
算牌與下注
步驟:
 記住21點要牌基本策略
 
練習在25秒內可以算完一副牌. 1 牌與-1牌成對出現時結果為零,自動去掉,這樣可以提高算牌速度
 
在賭場裡, 當發出牌的平均加減總額為2或大於2時,開始下注,平均加減總額大與4時增加賭注。平均加減總額是指實際加減總額除以剩下牌的副數,因此算牌過程中要時常注意大約還剩下多少副牌沒發。

二十一點算牌與下注技巧(英文)


Card counting? Don’t you have to be some sort of mathematical genius or have a photographic memory to count cards?

Not really. Even if the casino is using multiple decks, keeping track of the cards is a only a matter of counting. All you really need to count cards is the ability to count up to plus or minus twelve or so… by ones.

The first card counting systems were developed by our old friend Dr. Thorp. He determined through mathematical computation that the card that has the most influence on the deck being in a favorable condition (for the player) was the five. When the deck is low in fives, the player has a higher advantage than if it’s sparse in any other card. Logic dictated that for a very simple card counting strategy, simply keep track of the abundance (or lack thereof) of fives. This is the basis of his “Five Count” system which was later improved to include tens and renamed the “Ten Count” system.

Today, there are many different card counting systems. Typically, the more complex a system is, the better your advantage should you master it. However, the difference between card counting System X and System Y is usually so small that ease of using the system becomes more important than gaining an additional .15 % advantage (or whatever it is). This discussion is restricted to a single card counting system: the high/low (also called the plus/minus) point count. This strategy is very easy to master. Two other methods that I recommend if you’re serious are the Advanced Plus/Minus and the “Hi-Opt I” systems. The former is similar to the high/low but assigns fractional values to certain cards as opposed to integer values which are easier to add in your head. The latter method is considered one of the most powerful counting systems of all time.

The quick and dirty reason why card counting works is this: The player gains an advantage when a deck has a shortage of cards valued 2, 3, 4, 5, 6, 7, 8. When a deck has a shortage of cards valued 9, 10, Ace; the player has a disadvantage. If you can tell when the deck is rich in 9’s, 10’s, and Aces you can do one of the following things:

  • Bet more money when the deck is favorable to you.
  • Alter your Basic Strategy play to account for the favorability, thereby increasing the odds of winning a particular hand.

Now lets discuss the /- Point Count. As you can see from the small chart below, a plus value is given to low cards, and a minus value is given to high cards. Notice that 7, 8, and 9 have a value of zero. This is because their overall effect is negligible as compared to the others. Some systems use a value of -2 for the Ace instead of -1 and give a value of 1 to the seven instead of zero.

PLUS ( 1)
MINUS (-1)
2 | 3 | 4 | 5 | 6
7 | 8 | 9 | 10 | A
1 | 1 | 1 | 1 | 1
0 | 0 | 0 | 1 | 1

As you may notice, this is a balanced system. There are 20 cards in a deck that are valued 1: two through six. There are 16 ten value cards and 4 Aces in a deck (20 total) that are valued -1. The remaining 12 cards (7, 8, 9) have a value of zero. At the end of a deck the count should be zero. A good drill to practice is to get a deck of cards, turn them over one by one, and keep track of the count. If you enter a game mid-way between the deck or shoe, flat bet until the cards are shuffled. Once the cards are shuffled commence counting from zero.

A quick example using ten cards: the following cards are shown in the course of a hand: A, 4, 7, 10, 10, 9, 10, 2, 10, 5. The first value is -1 (the Ace) & the second is 1 (the 4) = 0 (the current total hand count). The next card is the 7 which is zero so disregard it. The next card is a ten so the total count is now -1. The next card is another ten, giving a total count of -2. The next card is a nine which has a value of zero so ignore it, total count is still at -2. Next is a ten, total count is at -3. Next is a two which adds 1 to the minus three yielding a total of -2. A quick look at the next two cards shows that the two will cancel each other out (-1 1=0). So at the end of a hand of ten cards dealt to 2 players and the dealer, the point count is minus two. This provides you with the knowledge that your are at a slight disadvantage. Your next bet should either be the same or a unit or two lower.

From this example you see that it would be easier to count cards if you play in a “cards-up” game. That way you can see all the cards as they are dealt and count them as they go by. When the dealer deals fast, just count every two cards. You still count each card but you only add to your total count after every two cards since many times the two values will cancel each other out to give a net value of zero, which doesn’t need to be added to your total. If you play in a cards-down game, you may want to consider playing at third base. The reason being is that in a cards-down game you only see the other players’ cards:

  • if you peek at their hand (not polite but it’s not cheating like in poker)
  • if a player busts
  • when the dealer settles each players’ hand.

When there are other people at a table, all this happens rather quickly and you may miss a few cards here and there, which essentially invalidates your count. You can’t control how fast the dealer deals, but you can slow things down when the dealer prompts you for a play decision.

For one deck, alter your wager according to the following table:

Bet Units /- Running Counts
1
2
3
4
5
1 or less
2 or 3
4 or 5
6 or 7
8 or more

Example: After the first hand of a one deck game, the point count is plus four and you just bet a $5.00 chip. Before the next hand is dealt, wager $15.00 (three units of $5.00) as the above table mandates.

What if there are four, six, or more decks instead of just one? I recommend that you perform a “true-count” rather than trying to remember different betting strategies for different number of deck games. By doing a true count, the above table can still be used.

The True Count is found with the equation below. I provide an example along with it for the case of having a running count of 9 with one and a half decks left unplayed. It doesn’t matter how many decks are used, you just have to have a good eye at guesstimating the number of decks that are left in the shoe. I just measured the thickness of a deck of cards to be 5/8 (10/16) of an inch. Hence the thickness of a half deck is 5/16 of an inch. One and a half decks would be 10/16 10/16 5/16 = 25/16 or a little over an inch and a half. You probably see a relationship here. The number of decks is approximately equal to the height of the cards in inches.

true count

Looking at the table of betting units above, the proper wager would be four units.

If you have trouble keeping the count straight in your head, you can use your chips as a memory storage device. After every hand tally up the net count and update the running or true count by rearranging your chips.

One last thing. There is no law or rule that says a dealer cannot count cards. A dealer may count cards because he or she is bored but more likely is that the casino may encourage counting. The reason being that if the deck is favorable to the player, the house can know this and “shuffle up”. This is also called preferential shuffling (a game control measure) and it vaporizes your advantage.