Poker Math Lesson 201: Drawing Hands vs. Made Hands

Hello math fanatics, I hope your brain has had a chance to recuperate from my study on pot odds and counting outs. We'll be building on that foundation in this article as we discuss drawing hands vs. made hands. It would be difficult to exaggerate the importance of this subject. Most players know very little about these, inevitable, confrontations form a mathematics point of view. For that reason, even a remedial understanding of poker statistics will allow us to show a profit when we are drawing and when our opponents are drawing against us. I'll try to provide that understanding in this article.

Drawing and Made Hands

Because NLH (No Limit Hold 'em) is the most popular form of poker, I'll use it for most of my examples but the information contained in this article can be applied to all forms of poker. Largely poker pots are contested between made hands and drawing hands. For example, I have flopped top pair top kicker in NLH, and you have made a draw to the nut flush. That's where a lot of tough decisions come from in poker, and where a lot of the mistakes are made. I'm going to teach you how to make good decisions in that area and how to exploit your opponents' mistakes.

Let's start with an example from NLH; you are in the early stages of a tournament, with blinds at 10-20 and 1500 in starting chips. You have opened the pot for 60 from first position with AhKc. Everyone folds to the small blind who calls the raise, the big blind also calls. The flop comes; Ad Kd 5h, giving you top two pair. The pot contains 180 chips, both players check to you. Now what? The mistake I see a lot of amateur players make is to slow play in these situations. Some players would make a very small bet in the pot to try to extract some value, maybe 60 chips. Some players might even check the hand to try to induce a bluff on the turn. If that's you, stop it. Checking a flop like that is an extraordinary mistake that's going to cost you big time. When you think of the types of hands that might have called you from the blinds you can see what kind of danger your strong, but vulnerable, two pair might be in. Any two diamond combination gives your opponent a flush draw, JT or QJ gives your opponent a straight draw and any pocket pair could make a set to beat you. There is no way you should give a free card on a flop like that. So how much should you bet?

Let's look at the math. If your opponent is drawing to a flush (worst case scenario) he or she is going to "get there" on the turn one time in five so the odds are 4 to 1 against. We have to make a bet that makes calling with those odds a mistake, then we hope for a call. If we bet the pot we are offering only 3 to 1 pot odds so a bet of 80 chips is enough to price the draw out assuming we are not going to put any more money in the pot if we lose. The problem is that you have a hand that's strong enough to warrant a call on the end even if a third flush card is exposed. So, if we bet 80 chips we give our opponent a chance to call 80 chips into a 240 chip pot (3 to 1). That would be a mistake if he could win nothing more in the hand; however, we will have to pay off at least a small bet at the end if he gets there. I think a better bet is 160 chips. When the board offers a range of draws you must protect your strong hands by betting. Betting the size of the pot only offers those draws a price of 2 to 1 and makes calling a huge mistake, and they will call.

What if we turn the tables? Let's suppose you are drawing to the nut flush and your opponent makes a bet into a 160 chip pot. How much can you afford to call? The answer really depends on a number of different factors. One of those factors is the size of the blinds relative to the stack sizes, and another is how loose calling our opponent is. We are only going to fill a hand one time in five trials so we need to be able to make more than four times our investment when we do hit to warrant a call. If there are 160 chips in the pot now and my opponent bets 80 chips, I'm only getting a price of 3 to 1 from the pot so my call has a negative EV based on pot odds alone. However, I know that the pot I'm after has the potential to become much larger than it is now, and I'm playing for that pot, the "implied pot". You should factor in the number of chips you can expect to win on future betting rounds into the pot before deciding whether or not to play. Against a very tight player I usually won't call any more than the size of the pot on a flush or open-ended straight draw. If my opponent is very loose and reckless and can be expected to bluff or call off a lot of his chips if I make my hand, I'm sometimes willing to play for 2 to 1, calling a pot sized bet. For me to call a pot sized bet on a draw the situation has to be just right. That call is counting on massive "implied odds" (the money that is not in the pot now but that can be extracted on future rounds). I'd have to be playing in the very early stages of a tournament against a player who might even let me bust him in order to call a pot sized bet on a flush draw.

In general, when you are drawing to a good flush or an open-ended straight you can afford to call any bet that is the size of the pot or less. When you are trying to protect your hand against a scary board that offers potential draws you should bet around the size of the pot to punish players to draw against you. I like to bet the size of the pot if I think my opponent is drawing, this give him an opportunity to make a large mistake, the pot sized bet will usually be called by drawing players, which is what you want. If you make a bet size that's too large, you run the risk of chasing them off. Remember we don't necessarily want to get rid of the draws, we actually want to offer them a mathematically poor wager and hope they take us up. The pot sized bet usually accomplishes this well. Remember, poker is largely a game of Made hands vs. Drawing hands. Good players can learn to profit from both. Good "luck".

Poker Math Series by Dead Money

Poker Math

Poker Math 101: Pot Odds and Counting Outs
Poker Math 201: Drawing Hands vs. Made Hands
Poker Math 301: Starting Hand Odds
Poker Math 401: Application of Knowledge
Poker Math 501: End Game Mathematics

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