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n a pair of the same denomination as the triplet would require play something like what we hear of in old Mississippi stories, where a 'straight flush' would be met by a very full pair of hands, to wit, five in one hand and a revolver in the other ! The total expectation of improvement is 1 to 8; but then see what an impression you make by a draw which means a good hand. Then, too, you may suggest a yet better hand, without much impairing your chance of improvement, by drawing one card only. This gives you one chance in 47 of making fours, and 1 in 16 of picking up one of the three cards of the same
denomination as the odd cards you retain. This is a chance of 1 in 12.
'Draws to straights and flushes are usually dearly purchased,' says our oracle; 'always so at a small table. Their value increases directly as the number of players.' (The word ' directly' is here incorrectly used; the value increases as the number of players, but not directly as the number.) Of course in drawing to a two-ended straight, that is one which does not begin or end with an ace, the chance of success is represented by 8 in 47, for there are 47 cards outside your original hand of which only eight are good to complete the straight. For a one-end straight the chance is but 4 in 47: with a small chance, to% of improving your hand, you are trying for a hand better than you want in any but a large company. ' If you play in a large party,' says ' The Complete Poker Player,' ' say seven or eight, and find occasion to draw for a straight against six players, do so by all means, even if you split aces.' The advice is sound. Under the circumstances you need a better hand than ace-pair to give you your fair sixth share of the chances.
As to flushes your chances are better, when you have already four of a suit. You discard one, and out of the remaining 47 cards any one of nine will make your flush for you. Your chance then is 1 in 5 2/9. In dealing with this point our oracle goes altogether wrong, and adopts a principle so inconsistent with the doctrine of probabilities as to show that, though he knows much more than Steinmetz, he still labors under somewhat
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