引用:
原帖由 細摩 於 2007-3-26 12:10 發表
可唔可以講多o的黎聽下??
See below. 唔好見笑。純粹交流分享，千祈唔好當貼士，後果自負。
My methodology is:
First since normally (at least in the typical casinos e.g Sands) every gambling table will use 5 decks in total, hence for simplicity I ignore the appearances of those cards which are already on the table and take the probabilities of every card as its original proportion in the deck i.e. for A, 2 to 9, the probability is 1/13 or 7.69% while that of 10 is 4/13 or 30.77%
Next, I attempted to calculate the probabilities of dealer's final points (17,18,19,20,21 or >21) for each value of his face card (A, 2, 3....., 10), by summation and multiplication of all the conditional probabilities This is easy since the dealer has no discretion but has to hit until he got 17 or above and has to stay after getting that.
Next I come to the player's side and, by the same method of summation and multiplication of all the conditional probabilities, I attempted to calculate the expected payoff for every initial points of the player's first two cards (2, 3, 4, ...18, 19, 20). I assume I bet $100 per game and the payoffs (ignoring the initial bet of $100 which is sunk anyway) of lose, draw, win and surrender, are $0, $100, $200 and $50 respectively. This exercise is more tricky as the player has the choice of hit or stay at every decision making node and he also has the additional option of "surrender" and "double" in the initial decision node and "split" if he got a pair. (I assume the game adopts the typical US Black Jack rule as adopted in the Sands casino in Macau i.e. you are at liberty to double up your bet regardless of your initial points. I am aware in some casinos .e.g Lisboa, you are only allowed to double up if you got 11 initial points. Personally I prefer the former).
The criteria I applied in making that decision is to compare the expected payoff of each optioin. i.e. If the dealer's face card is 10 and I already got 16, since the expected payoff of hitting is slightly higher than the expected payoff of staying, I would assume in that case ( i.e. dealer's face card is 10) the player will hit anyway if he got 16. Of course if he got 16 already with his initial two cards, he should surrender as the payoff of surrender is $50 while the expected payoff of hit is only $43.07 (although it is higher than the expected payoff of stay which is $42.42).
By following the above methodology, I came up with the optimal strategy. which can be summarised as follows:
Basically the guiding principle is: the stronger the dealer's face card (i.e. it's relatively less likely he will burst), we should adopt a more progressive tactic to hit in order to defeat the dealer. In contrast, the weaker the dealer's face card ( i.e. it's relatively more likely for him to bust), we should be more defensive and conservative i.e. we should stay at a lower point levels to avoid getting bust ourselves and should let the dealer bust.
In general:
(A) Dealer is strong if his face card is: A, 10, 9, 8 and 7 (in order of strength)
(B) Dealer is weak if his face card is: 2, 3, 4, 6, 5 (in order of strength)
If the dealer is strong (i.e. his face card is A, 10, 9, 8 or 7)
Hit or StandFor 7, 8, 9, 10, we should hit until we got 17 or above. For A, we should hit until we got 15 or above (the intuition is that for A, it is relatively much more likely that the dealer will get Black Jack hence the potential benefit of hitting above certain level, namely 15, diminished).
Surrender:For A, we are not allowed to surrender but have to hit until 15 or above as said.
For 10, we better surrender if we got 12 to 16 as the expected payoff is less than $50 which is the payoff of surrender.
For 9, we better surrender if we got 16 for the same reason.
For 7 or 8, the dealer is relatively weaker compared to 9, 10 & A and we shouldn't surrender but should hit until we got 17 or
above.
Double up:We should never double-up our bet even if we got the strongest initial points (i.e. 11). The dealer is simply too strong here.
Split: We should only split if we get a pair of Ace.
If the dealer is weak, (i.e. his face card is 2,3,4,5 or 6)
Hit or StandFor 3,4,5 or 6, we should stay and avoid to get burst once we got 12 or above. For 2, the dealer is relatively stronger than 3,4,5 and 6 and we should be a little bit more progressive to hit until we get 13 or above.
Surrender: Since in this case the dealer is weak, we should never surrender.
Double up: For 4, 5 or 6, the dealer is weakest, hence we should double up if we get 9,10 or 11 at the beginning. For 2 or 3, the dealer is a little bit stronger and henc we should only double up our bet if we get 10 or 11.
Split: Again we should only split if we get a pair of Ace at the beginning.
That's it.
