So you see your two initial cards and the dealer's starting card. Sooner or later, he will start to collect his card combination and end up getting from 17 to 21 points or running into a bust.
The probabilities of different outcomes depending on the dealer's card are shown in Table 1.
Obviously, the dealer's starting cards are not equal. The first (and fairly accurate) idea of the strength of his card can be obtained from the "Overkill" column. The strongest card is ace, the weakest is 6. And if you line up the cards in decreasing order of strength, we get the sequence
T, 10, 9, 8, 7, 2, 3, 4, 5, 6,
although a more accurate analysis leads to a slightly different result:
T, 10, 9, 8, 2, 3, 7, 4, 5, 6.
Now let's look at the player's cards and try to understand whether it is worth taking an additional card or it is better to stop. If blackjack has come, there is nothing to talk about, if 19 or 20 points is also not bad, and a new card is not needed. Although it is easy to deduce from Table 1 that the dealer's chances of getting an ace or ten are slightly higher than that of a player with 19 points.
Let's assume for now that you don't have an ace: the double-valued aces (1 or 11 points) requires a separate approach. It can be proved that it is not profitable to take a card with 17 or 18 points. On the contrary, if you have 11 points or less, you must take a card. This is quite obvious: you are insured against busting, and a new card will not reduce points.
12-16 points is a difficult situation: your chances are slim, and your strategy should depend on the dealer's card. Let's say he has an ace and you have 16 points. Only in 5 cases out of 13 a new card (2, 3, 4, 5 or ace) will improve your combination, in the remaining 8 cases you will be bust (6, 7, 8, 9 and four tens). Therefore, it seems that taking a card is insane. But this is not so: the dealer's card is very strong and the situation is so difficult that the risk is simply necessary. This typical "gambling" reasoning is confirmed, of course, by mathematics. If you give up the extra card, you will lose (on average) 76.94 cents on every dollar, and the “risky” decision will reduce the loss to 66.57 cents. The stronger the dealer's card, the more justified the risk.
The strategy of an additional set of cards is shown in Table 2 ("+" - take a card, "-" - stop). If at least one of the player's two initial cards is an ace, we use Table 3. It is essential that the set of all subsequent cards is also based on these two tables corresponding to hard and soft combinations. Sometimes tables have to be used interchangeably. The fact is that hard combinations can turn into soft ones, and vice versa.
Source: https://stargambling.net/games/blackjack/
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