are many forms of draw poker and I will have something to say
about several of them, but there are a few considerations that apply
to every form of draw poker and I will discuss those first.
draw. If your object is merely to improve your hand, there is no
question that you are best off making the maximum draw: that is, three
cards when you have a pair, or two cards when you have three of a kind.
That does not
answer the entire question, however. Many times your
object will not be simply to improve your hand. Perhaps you will need
some specific degree of improvement, and perhaps it will be more
important to deceive the other players than to improve your hand.
consider the case in which you need some specific degree of
improvement. Suppose you know, no matter how, that you need two very
high pairs—preferably aces up—to have a chance of winning the pot. You
have a pair, but it isn't high enough, even if you catch another pair.
Your three unmatched cards include an ace. This is a classic
case—should you draw three cards to the pair or should you draw two
cards to the pair and the ace kicker?
hold the ace kicker, the odds are only about 4 to 1 against your
getting aces up or better; if you do not hold the ace kicker, the odds
are about 51/2 to 1 against your getting aces up or better. This is one
of the rare cases in which it pays to hold a kicker. But you have to be
quite sure that aces up, specifically, is the hand you want. Every so
often, when you do make aces up by holding the kicker, your opponent
will fill his full house and ruin you (this will happen almost
precisely once in twelve times) and your three-card draw will give you
about ten times as good a chance of making an even better hand and
beating him on those few occasions. Holding the ace kicker is almost
the only case I know in which a special draw has a mathematical
advantage over the customary draw, and even here I know many good poker
players who would rather draw three cards to the pair and take their
chances on the many added opportunities to draw a still better hand,
three of a kind or a full house or even four of a kind.
suppose your purpose is not to improve but to keep the opponents
guessing. This case arises chiefly when your original
hand is probably better than any hand another player will draw. The
simplest possible example, but probably the least useful, would arise
when you are dealt four of a kind. (It is the least useful example
because it will happen so seldom.) You have a choice between drawing
one card and standing pat. Your decision depends entirely upon the
betting before the draw. If the betting includes two or three raises,
and you think there are strong hands out against you, your best chance
is to stand pat. You will then be figured for a straight, since
straights constitute well over 50 percent of all the pat hands that are
dealt. A player who makes a high straight, a flush, or a full house
will surely call a bet, will usually stand a raise, and with the better
hands will reraise and then call your second raise. However, if you are
up against weak hands before the draw and have simply raised once, you
are better off to draw one card. You will then get a call on two high
pair, a possible raise on three of a kind, and tremendous action on a
full house, especially if it is a high one.
said, knowledge of how to play a pat four of a kind isn't going to
be of much moment in your practical poker play. Knowledge of how to
draw to three of a kind is going to be of tremendous importance.
there were not so many exceptions (poker being a game of infinite
variety) I would say flatly that for tactical purposes one card should
always be drawn to three of a kind even though mathematics favors the
two-card draw. Very seldom do you have a chance to play three of a kind
any differently from two pairs before the draw. Getting called after
the draw may depend largely on making the other players think your hand
was two pair rather than three of a kind going in. A one-card draw
represents a special advantage in draw poker, and any player who draws
one card and is in any kind of good position will find the other
players checking to him, giving him the maximum opportunity to make the
important things to remember about three of a kind are these:
Unless you have more than three opponents, your hand will probably be
best at the showdown even if you do not improve it. While a two-card
draw gives you a much better chance to make four of a kind and a
slightly better chance to show some improvement, in most hands it would
not matter if you drew one card, or two cards, or stood pat, you would
the draw to three of a kind is partly a matter of
your individual tactics and your recent history in the game. If you
have not represented the hand too strongly before the draw, and if you
are a player who has been detected once or twice recently drawing two
cards to a pair and a kicker, then the two-card draw will be tactically
the best. Your chance of improvement is at the maximum and you are
likely to get called by players who suspect you of bluffing. If you
have been called in one or two pat-hand bluffs, that is an admirable
time to stand pat on three of a kind. They will probably win without
improvement and you may get a call. But year in, year out, without
background, the one-card draw will work out best.
four-card straight or flush cannot possibly represent any problem.
You draw one card. Ninety-nine percent of the times, two pairs
represent no problem either; you draw one card. There is a very slight
exception in the case of two pairs. If you have two pairs that will
probably win without improvement (for example, against one or two
players who have not represented any great strength before the draw)
and if you think they might suspect you of a pat-hand bluff, you might
consider occasionally standing pat on your two high pairs, which should
be no lower than queens up. As a matter of fact, it is good tactics to
do this occasionally to give variety to your game and to keep the
op¬ponents guessing both when you have a genuine pat hand and when you
are trying a pat-hand bluff; but be sure to treat this as a method of
bluffing and not as a legitimate method of play¬ing poker. Like
anything unnatural in poker, it will not win if employed too often.
occupy a unique place in poker. Against one opponent and often
against two, aces have a better-than-even chance to win unimproved. If
you are the last man to speak before the draw, and two other players
are in, and you have a pair of aces, you might consider simply staying
in and drawing one card. This is especially effective as the aftermath
of two or three conspicuous cases in which you have drawn to a
straight or flush possibility and have failed to fill. If both the
players before you draw three cards, you draw one and bet; you may get
a sus¬picious call from one of the three-card draws, even if he does
not improve. The odds against your improving aces on a one-card draw is
less than 5 to 1 against you, while the odds are 21/2 to 1 against you
even if you drew three cards. Often such a mathematical disadvantage
can be sustained in the interests of better tactics.
In one sense, these should hardly be worth discussing. If
you have to make a freak draw, you shouldn't have been in there in the
first place. Nevertheless, occasions do arise (some of them
legitimately) when you have to make a freak draw, and the following
general advice can be given:
five-card draw is incredible, even when (as in many blind-opening
games) you got 7 to 1 odds to go in against one opponent.
better to draw four to an ace, if the rules of the game permit a
four-card draw, than to draw three to an ace-king.
better to draw two cards to three cards in sequence if A-K-Q, or
K-Q-J, or Q-J-1O, than to draw two cards to a possible flush such as
J-8-7 of diamonds. One of the possibilities is that you will make one
high pair or two pairs and that they will win, while the chances of
making the actual straight or flush are almost too remote to be
draw of one card to an inside straight is almost always wrong. The
odds against making it are almost 11 to 1. Few are the hands that do
not offer at least as good odds on making a single high pair or two
pairs if you simply throw away all the unlikely cards and draw four
cards to the highest card or three cards to some freak combination such
as a king and jack of the same suit. The inside straight is justly
notorious in poker. Almost the only case in which you draw one card to
an inside straight is the case in which you hold something like 9-8-6-5
or lower and know that even pairing your high cards will not give you a
chance to win. Even so, you can draw four cards to your highest card
and have a l-in-12 chance to make two pair or better—the same chance
you have when you draw one card to an inside straight.
closing pages of this website are tables
of the mathematical odds
that tell your exact chances on most of these combinations.
paid no attention here to the question of drawing when there is
a wild card in the game, such as the bug or the joker, because all such
cases will be taken up separately.
strength of your hand. The first thing to remember in draw
poker, and in nearly any poker game, is that the best hand going in is
usually the best hand coming out. The next thing to remember is that
the more players who stay against the best hand, the fewer pots it will
win but the more money it will win.
exception to this is the case of two low pairs, a special hand
that I will discuss separately.
of your hand in draw poker depends entirely on the number
of players who have not dropped.
proved to be a difficult concept for many poker players and I
will try to explain it in this way: Mathematicians have worked out the
hand that is likely to be highest in a game of any given number of
players, for example eight players, or four players, or only two
players. When a player before you has dropped out, from the
mathematical standpoint you can forget that he was ever in the game.
Consider only the players who are yet to speak. As a simple example, in
an eight-handed game of draw poker it takes two aces to have a
better-than-average chance of being the high hand; but if you are the
seventh man, and the first six have already dropped, and you have only
the eighth man to contend with, the mathematics of the situation become
precisely the same as if you were playing in a two-handed game and the
first six players had never existed. In that case, two deuces or an A-K
high will have a better-than-even chance of being the high hand.
If you have
absorbed that, you can follow the table below, which tells
what you have to have to have a good chance against any given number of
players who are yet to be heard from:
|Number of Players Yet to Speak
||Hand with Better than 50% Chance
of Being High
||2 Deuces or A-K high
certain games, in which the overhead is high (as explained in the
section on "Money Management"), you must make
the opening bet on such a
hand to give yourself a better-than-average chance to win in the game.
In games in which the overhead is low, you can afford to be more
conservative (and winning players usually are somewhat more
conservative); for example, you can refuse to open in any but the last
three positions on anything less than aces, and you can refuse to open
in the last three positions on anything less than queens. I do that
myself, except in a jackpots game, in which I will open in last or
next-to-last position on the minimum of jacks and take my
chances on the possibility that some earlier player was sandbagging.
If I do open on jacks and an earlier player stays and draws three
cards, I tend to draw one card and bet, representing two pair and
trusting that my opponent will not have the acumen to raise me and
force me to drop if he does not improve.
If he raises me and I have not
improved, I usually drop. I may lose to a bluff occasionally, but I
more than make it up in the cases in which I actually did have my two
pair or a better hand and can legitimately call his bluff.
mathematical figure in poker must be modified by later
information. The mathematicians work on the basis known as a priori
(meaning before the expected event has actually happened). Most of
poker would be termed by mathematicians a posteriori (meaning that the
calculations are made when actual information is already available). If
you are the last hand in a seven-man game and the third man has opened
and the fifth man has stayed and the others have dropped, you must know
(if the game is reasonably strong) that there is at least a pair of
kings out against you. You will not stay on less than two aces or two
low pairs, in spite of any number of mathematical tables that tell you
that two eights stand a chance to win against two opponents.
in a wide-open game in which a player cannot bear to throw away a pair
of tens or a four-flush, you may choose to stay on a little less.
game, no one bets against a one-card draw with less than
three of a kind or aces up, and if the one-card draw bets or raises, no
one raises it without a flush. If the one-card draw reraises, he filled
at least an A-Q or A-K flush and a possible full house, and his raise
cannot be reraised without at least jacks or queens full. The profits
in poker come from getting a call when you have a slightly better hand
than your opponent; they are dissipated chiefly by the occasional chip
thrown away in staying on a losing hand or calling on a doubtful hand,
but they can be as easily dissipated, and much faster, by giving a very
strong hand a chance to raise or reraise and then calling.
depends on appraising your opponent that it is hard to
generalize. A poor player will become overly enthusiastic when he has a
good hand; he will become almost unrestrainable when he has made that
another diamond. It might be the better part of valor
merely to call him on a low full house, but it would be stupid to drop
a low full house or an A-Q flush on his second raise, on the grounds
that an intelligent player would have been fearful even of calling on
A very good player, however, when he raises the bet of a hand
that represented two pairs going in and drew one card, should not be
called on less than jacks or queens full. Against such a player, there
will be a net gain in the long run by throwing away a straight.
that when there is action in the pot, there are three hands
worth staying on: Two aces, but no lower pair; if the aces improve,
they have an excellent chance of being high. A straight or flush draw
if the pot offers substantially more than the odds against filling—that
is, 6 or 7 to 1, as against the 4- or 5-to-l odds against filling. And,
third, a good hand going in— no less than queens up or a low three of a
kind. A lower pair than aces, and especially two low pairs, are
candidates for the trash can.
3. The play
of two pair. Some authorities have said that 90 percent of
one's winnings or losses in poker can be attributed to the play of two
low pairs (no higher than tens up). This is undoubtedly an
exaggeration, but it serves to emphasize an important point.
principle governing the play of two pair is this: Before the
draw, the odds are nearly 2 to 1 (in any draw game) that any two pair
will be the highest hand. But the odds are 11 to 1 against improving.
two low pairs have a better-than-average chance of
standing up (without improvement) against one or two opponents; they
stand to lose if three or more opponents are in the pot. Queens up is
the lowest hand that stands to win against three opponents, and aces up
against four opponents. This takes into consideration the chance, one
in twelve, of improving the two pairs you are dealt.
knowledge has been derived a general rule that has almost
become a poker precept: If you have two pair, raise at once, so as to
drive out as many as possible of the other players.
that a raise tends to drive other players out and that you
want other players driven out when you have two low pairs.
Nevertheless, the rule is faulty. You should raise only when you are
the second man (the one next to the opener). You should merely stay
when two players are in before you. You should drop
two low pairs when there are three players in before you.
When I say two low pairs, I mean in this case anything less than queens
up. I am also assuming that the pot is offering you no more than 6 to
1. With two low pairs against three preceding players, in a reasonably
tight game, the odds are better than 2 to 1 that one of them will
improve and beat you even if none of them has you beaten going in—and
my experience is that one of them probably has you beaten going in,
because there simply aren't enough high pairs around to give each of
three intelligent players a high pair that would justify his playing.
other side of the medal, much money is lost by failure to
back two low pairs strongly enough against one or two players who drew
three cards. If you have created doubt in their minds by an occasional
unsound one-card draw or bluff, and if you have stayed after both are
in, a one-card draw and a bet may get a call from a hand that did not
improve. When two opponents draw three cards each, it is better than
even that neither of them improved, and when you have a
better-than-even shot and can get a call from an unimproved hand, you
have a good bet. But if you are known as a man who would not play "on
the come" in second position, or if it is known that you would not open
on a mere possibility, or if you are in a jackpots game in which you
could not legally do so, do not bet; no one will call unless he can
beat you. You have to be the third man to speak.
two pair, the thing to watch out for chiefly is the case in
which the opponent will not call unless he improved and can beat you if
he did. For example, you open on two pair and draw one card. One player
stays against you and draws three cards. If you do not improve, a bet
is futile. He knows you would not have opened on less than two pair,
and he will not call unless he has improved and has at least two pair
himself. Against a good player, betting out on the opening hand in such
a position leaves you wide open to a reraise, which can be a very
successful bluff if your opponent has you figured correctly.
should seldom be opened in a "pass and back in" game. The
absence of high cards in the hand makes it more likely that another
player will have a high pair and will open; and of all hands, two pair
is the hand on which you want if possible to be the last to speak.
Queens up or better may be
should be opened if the overhead is high and the antes are
worth grabbing, but many good players simply do not open on any
two-pair hand under aces up if they are earlier than fourth from the
and out" game, you must open on any two pair in any
position. Your hand figures to be the best around the table and you
cannot afford to toss in the best hand. Just remember to be oh, so
careful in playing them afterward. Except in a wild game in which
players raise on single pairs and four-flushes, no two pair lower than
kings up can stand a raise.
establish queens up as the minimum for two "high" pairs?
Because in most games I have observed players opening on jacks and
staying on queens. If one of these hands draws a second pair, you will
want to have a chance.
summarize the play of two pair in the average draw game. In a
"pass and out" game, open. Next to the opener, raise. Separated by more
than one active player from the opener, never raise and consider
(depending on the game) whether or not you should drop. Do not stand a
raise in any case in which three players are in the pot ahead of you,
and do not stand a raise on less than jacks up unless the raise was
made by the player next to the opener.
of a kind. In a game of draw poker, any three of a kind
figure to be best before the draw four times out of five. The advantage
of three of a kind is that they will usually win without improvement
and if improved they may win a big pot. The disadvantage of three of a
kind is that the odds are at best (with a two-card draw) about 81/2 to
1 against improving, and since three of a kind can be played strongly
before the draw, the loss is heavy whenever another player draws out on
you. A low three of a kind are not worth betting (after the draw)
against more than two three-card draws or against more than one
reason, a low three of a kind (lower than tens) should be
played before the draw about the same as two high pairs. Raise fast,
drive out other players, limit the number of other players who will
draw against you.
discussed the draw to three of a kind elsewhere; but to repeat,
a hand that is opened on a low three of a kind and has not been raised
should usually draw one card and bet. He will get calls from two high
pairs, and he is likely to get a call rather than a raise from a
straight or flush that has filled, for fear he too
has filled (a full house) and can raise back.
split two pairs unless
you know an
openers only to draw to a straight
|Draw one—but do not
openers to draw to
straight or flush.
wild—draw two to the A-A-2 unless
have been several raises, in
draw one to a
the six of hearts and draw one
card to the straight flush,
|The joker is
the bug—draw three cards to
|| The joker
is the bug—draw two cards to
bug, ace, jack.
|The joker is
the bug—usually draw one to
|| The joker is the
two to the bug and pair.
opened, draw three. If another
opened, draw one.
opened, draw one. (In Blind
Opening, against one
opponent, draw three.)
chance of a higher pair is reduced
the A-K holding.
unless dealer or next to dealer;
someone else should open.
A hand with a
low three of a kind that has been raised before the draw
and has not raised back (and usually, low threes should not raise back)
will do best to draw two cards, look at his draw, and bet. This is
especially true if the raiser drew one card. The raiser may call on two
high pairs, and he may figure the opener to have drawn to a pair and an
kind from jacks to aces are worth a reraise before the draw.
Having reraised, the hand almost must draw two cards, for maximum
chance of improvement. However, the action here is affected by
position and the draw. If you are last to draw and speak with high
threes, and if you are up against two two-card draws or one two-card
and one one-card draw, you might do worse than to draw one card and
check on the grounds that you might as readily have raised back with
aces up. You might then get a bet against you on any threes. If, having
raised, you draw two cards and check, no one is going to bet into you
(unless he can beat you); if you bet, low threes probably will not call.
threes (at least queens, preferably kings or aces) it may pay
merely to call against two opponents or only one. You draw one card.
The raiser will probably bet into you.
"pass and back in" game, any three of a kind make a good
pass as first or second player after the dealer. Usually, nothing is
lost except the antes if nobody opens. Your position after the draw is
bound to be best, because you will be the last player from the opener
to speak. You have an automatic raise if two or three players come in.
You can choose instead to have an excellent positional advantage if
there are more than three players in: You refuse to raise, draw one
card, and can be figured by every other player for a possible straight
or flush draw (because there was so much money in the pot before you
came in). This will give you a big pot when you hit a full and one or
two players before you improved; it will often get you a call when you
bet as last man, since your bet might be on a busted straight or flush
draw; and you retain freedom to get out without further cost if there
is much action before the betting reaches you.
a kind it is most important not to find yourself in the
middle when the opener is on your right and there are one or more
one-card draws on your left. Much of the money lost on three of a kind
can be attributed to betting in such a case. In bad
position, you can only check three of a kind. A bet is
futile because the one-card draws have either busted and will drop, or
have filled and will call or raise and win; or will bluff and put you
in a most uncomfortable position.
further reason why it pays to check, rather than bet, when
you hold threes in a bad position (with active players both to your
left and to your right). If you check in that position, there will
often be a showdown and you will turn up with three of a kind that
obviously you had all along. Your opponents will remember this and you
will save yourself some problems when you have two pairs and wouldn't
know whether or not to call a speculative bet.
4. "Don't bet
into a one-card draw." This is the most useful and yet
the most costly of all poker precepts. If you never bet into a one-card
draw, you are unlikely to be a winner in a tight poker game. Yet
betting into a one-card draw is the most dangerous thing you can do in
poker. The decision has to be a matter of discrimination and
reconstruction of the opponent's probable hand. Before
deciding whether to bet or check (if permitted), consider the
hand the opponent is most likely to hold. This must necessarily depend
upon your appraisal of the opponent, but your appraisal can be a rough
one—he is known to be a wild and gambling player, or he is known to be
a conservative player. Strangely enough, you are safer betting into the
conservative player than into the gambling player, if you have two
high pairs or better.
Against the conservative player, aces up and
three of a kind are often equivalent; he didn't stay on less than two
pairs, and either of your possible hands will beat him if he calls.
Against the gambling player, aces up and three of a kind are still
equivalent. He may have drawn to a straight or flush, and if he hit he
can beat you and if he didn't he will throw his hand away. The moral is
nevertheless apparent. Against the conservative player, you can make
money by betting because you may get a call on a fair hand. Against the
gambling player, you can't make money by betting because he won't call
if he missed, and he will raise if he hit.
bet into a one-card draw is probably justified against one
or two opponents who probably stayed on sound hands; it is not
justified against a player who is wild and might have stayed on
anything, or against a
had to put in
and who might therefore have gone in on a straight or