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Odds of Hitting We already know the odds of one particular card coming out i.e. if we have 16 the chance of a 5 coming out is about 7.7% (assuming we see no other 5's out) but what is the chance over two cards we would hit 21? If we had an ace, 2, 3 or 4 we could potentially continue hitting in the hope of hitting 21 and hence the odds would change. What sort of information would be useful to making an informed decision? The odds of hitting 20 or 21 over two cards we have already established would be of some use. The odds of busting on a given hand value if te player decided to hit would also be of some use. As would the combined chance of hitting either 20 or 21. Below shows a table which can be used as reference in cases when a player has a certain hand value which can be used to make more informed decisions. For simplicity the chance over 1 card of hitting 20 or 21 has been excluded as it is easily worked out by the player. | Starting Hand Value | Chance of Hitting 20 over two cards (%) | Chance of Hitting 21 over two cards (%) | Chance of Hitting 20 or 21 over two cards (%) | Chance of Busting on First Card Taken (%) | | 20 | 100 | 7.7 | 107.7 | 92.3 | | 19 | 7.7 | 8.4 | 15.84 | 84.6 | | 18 | 8.4 | 8.88 | 17.02 | 76.9 | | 17 | 8.88 | 9.32 | 18.2 | 69.2 | | 16 | 9.32 | 10.07 | 19.39 | 55.2 | | 15 | 10.07 | 10.51 | 20.58 | 47.5 | | 14 | 10.51 | 11.25 | 21.76 | 39.8 | | 13 | 11.25 | 11.69 | 22.94 | 32.1 | | 12 | 11.69 | 12.43 | 24.12 | 24.4 | | 11 | 12.43 | 35.98 | 48.41 | 0 | | 10 | 35.98 | 16.43 | 52.4 | 0 | | 9 | 16.43 | 9.17 | 25.6 | 0 | | 8 | 9.17 | 9.46 | 18.63 | 0 | | 7 | 9.46 | 8.72 | 18.18 | 0 | | 6 | 8.72 | 8.28 | 17 | 0 |
Using this table it is a easier to say what is a worthwile call. If a player stands and has two cards and the card showing is a 8, you know the best hand he can have is 19 so you can work out your odds of getting a guaranteed better hand and the risk assocciated. Clearly 11 is such a strong hand as 50% of the time in two cards you will have a better hand guaranteed with 0% risk of busting on your first card. In contrast a value of 17 is looking shakey as only 18% of the time can you be certain of the win and you are about 70% favorite to bust on the first card you take. Of course your opponent may have stuck on 12, its difficult to say. This is where reading players comes in. |
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