Introduction
Development
Introducing Poker
Ranking Hands
Chips
The sequence of play
Shuffling
Dealing
Betting Interval
Betting Small and Big Blinds
Table stakes
Using wild cards
Probability of holding
First betting interval
Strategy-1
Strategy-2
Seven-Card Stud
Other forms of poker
Texas Hold'em Basic Hand
Five - Six card Omaha
Poker Sense
Slow Playing
Other Gambling Card Game
Blackjack
Brag
Seven-card Brag
Gin Rummy
Glossary

Odds of improving a hand in the draw

The better the hand you are dealt, the lower the odds of you improving it in the draw; the chances of improving your three of a kind in the draw are more than 8 to 1 against.
Usually the number of cards to exchange at the draw is obvious and straightforward. However, many poker players have differing views on the advisability of drawing two or three cards when holding a pair. Some players, with a hand like ♠ A, ♥ 10, ♣ 3, ♥ 2 would prefer to hold the pair and the ♠ A (the odd card in this situation is called a kicker ( see below) rather than draw three cards to the pair. Tables 5 and 6 indicate the approximate probability of improving the hand drawing either two or three cards. From these it can be seen that by drawing three cards to a pair, the chance of improving the hand is about 14 per cent better than if only two cards are drawn. However, more than half the time, the improvement will be to two pairs only (57 per cent with a draw of three and 66 per cent with a draw of two.)

Kickers

This shows why some player advise keeping the high card as a kicker rather than discarding it. If the player who held the ♠ A, ♥ 10, ♣ 3, 3, ♥ 2, ended with two pairs, then it is to be hoped that he kept his Ace kicker and drew two cards only, because if he had it is odds on that his top pair will be Aces, and if two pairs is to win the deal, to have two Aces almost guarantees success.

On balance, of course, the tables show that it is better it is better to draw three cards to a pair rather than two (provided there are no other possibilities to consider, such as a flush), but a good player will choose to hold a pair and a kicker from time to time in order to keep his opponents in doubt as to his habits. It is probably not worth keeping a kicker unless it is an Ace or King.

Improving three of a kind

Some players occasionally consider keeping a kicker when holding three of a kind. The chances of improving the hand are better if two cards are drawn, but the odds are interesting, as Table 7 and 8 show.
The interesting thing here is that by drawing two cards you more or less halve the odds against you of improving to four of a kind, but at the expense of slightly extending the odds against you of making a full house.
In this case, however, psychology comes in. A player who draws one card is often attempting to fill to a flush or straight, or to improve two pairs to full house. If a player bets heavily after drawing one card other players might assume he has succeeded in achieving one of those hands, since if he fails his hand will be no better than two pairs. Therefore a player who draws one card to three of a kind and fails, by betting heavily might persuade other players that he has at least a straight and win the pot by bluff.

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