The Draw To Threes

“Hold your hands,
Both you of my inclining, and the rest.”
Othello. Act I., Scene 2d.

When a player finds threes in his hand on the first deal, he at once recognizes the fact that it may be improved to either a full hand or fours. There is no other increase of value possible. Once in every twenty-three and a half times four of a kind may be made by drawing two cards to threes. Just twice as often, or about once in twelve times, a full hand may be made. It is possible, therefore, to improve this hand by drawing just once in every eight times.

A favorite, play is to retain an odd card, discarding and drawing one card, and thus accomplishing the valuable result of deceiving one’s rivals as to the strength of the hand. The probabilities of improving the hand are of course much less, four of a kind being possibly made in this way only once in forty-seven times. The one-card draw will result in a full hand about once in sixteen times. The one-card draw creates the impression that the hand is either a .straight, a flush, or two pairs. It seems to be the opinion of good judges that as three of a kind is nineteen times out of twenty a good enough hand to win the pot, it offers the possessor a very wide range for the exercise of his own judgment in the draw. It matters not how the draw is made, the hand is bound to remain good, and may be improved. For this reason the policy of masking the hand is often advisable; for the one-card draw especially is calculated to create an appearance of bluffing, indicating a draw to a bobtail straight or flush.
Some excellent authorities on poker say that with three of a kind it is almost always best to hold up a card and draw one.