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The computation
of the probabilities and odds involved in the drawing of two or
more cards is somewhat more complicated. Mathematically, the probability
that two or more independent events will occur is determined by
multiplying the individual probabilities of each event. It is sometimes
easier, however, to multiply together the individual probabilities
of each event not taking place (i.e., multiplying the chances of
failure) and subtracting this product from 1 to give the probability
that two or more independent events will occur.
We have already investigated the chances of improving a hand consisting
of three of a kind and a kicker. You hold three tens and discard
a five and a deuce and draw two cards. What are your chances of
making (a) four of a kind, (b) a full house, and (c) any improvements
?
(a) You hold three of the tens; on the first card drawn, the chances
against getting the fourth ten are 46 out of 47. On the second card
drawn they are 45 out of 46.
The chances of failure are 45 to 2 on, which means that it is 22.5
to 1 against drawing four of a kind.
Similarly the chances of making (b) a full house, and (c) any improvement,
can be computed. The odds against making a full house are 15.4 to
1; against making any improvement they are 8.6 to 1.
The following table expresses some of the other odds against improvement
in the draw:
One practical conclusion you will draw from this and the preceding
table is that keeping a kicker in most cases reduces the chance
of improvement. An exception is that keeping an Ace with a pair
improves the chance of beating an opponent who holds two pairs.
Apart from this, the usual reason for keeping a kicker is for variation
or deception.
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