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Draw Poker

There 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.

1. The 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.

First, 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?

If you 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.

Now 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.

As I 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.

If 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 best decision.

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 still win.

Therefore 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.

A 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.

Aces 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.

Freak draws. 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:

A 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.

It is 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.

It is 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 considered.

The 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.

In the closing pages of this website are tables of the mathematical odds that tell your exact chances on most of these combinations.

I have 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.

2. The 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.

The sole exception to this is the case of two low pairs, a special hand that I will discuss separately.
The strength of your hand in draw poker depends entirely on the number of players who have not dropped.
This has 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
6 or 7 2 Aces
2 Kings
4 2 Queens
3 2 Tens
2 2 Eights
1 2 Deuces or A-K high

In 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.

Every 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.

However, 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.

In a good 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.

Here so much 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
and catches 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 his hand.

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.

I would say 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.

The basic 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.

Mathematically, 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.

From this 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.

It is true 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.

Taking the 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.

In playing 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.

Two low pairs 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 opened, and 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 dealer.

In a "pass 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.

Why do I 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.

I will 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.

Play of three 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 one-card draw.

For this 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.
I have 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.


Draw one—do not
two pairs  unless you know an opponent has
two higher pairs.
Draw one—split
only to draw to a straight flush
Draw one—but do not
split openers to draw to
a straight or flush.
Deuces Wild

Deuces wild—draw two to the A-A-2 unless there have been several raises, in which case draw one to a royal flush. Deuces wild—discard the six of hearts and draw one card to the straight flush, flush or straight possibility.
Poker With The Bug

The joker is the bug—draw three cards to bug and ace. The joker is the bug—draw two cards to bug, ace, jack.

The joker is the bug—usually draw one to the two pair. The joker is the bug—usually draw
    two to the bug and pair.

Having opened, draw three.  If another player opened, draw one. Having opened, draw one. (In Blind
    Opening, against one opponent, draw three.)

Open; the chance of a higher pair is reduced by the A-K holding. Pass, 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 ace kicker.

Three of a 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.

With high 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.

However, in a "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.

With three of 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.

There is a 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.

Therefore, a 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 flush possibility.

Copyright 2006 - 2013 Content by Albert H. Morehead