I've been asked this so many times, I figured it was time to write an article on it.

"How do you figure out your odds to make your flush or straight so as to decide whether or not to chase?"

It's time to do some math…

THE RULE OF 4 AND 2

To start with, you need to figure out the chances of your hand actually hitting or improving, and to know that you know to get comfortable with the "Rule of 4 and 2."

Here's how it works.


HOW MANY OUTS DO YOU HAVE?

First, you need to figure out how many "Outs" you have to make the Flush or the Straight (or a winning hand).

To do that you need to base your calculation upon what you know, and that is the 2 cards in your hand and the flop ONLY.

Now, if someone shows his cards to you as they fold (or table talk about it) before you make your decision, then that's more information for you to consider.

"But, Professor. You know all of your 'outs' aren't alive. People probably folded some of them."

You're correct. However, you can't know this for certain, and as such, you can't speculate. It's likely NO ONE has folded your "outs" as well.

Granted, you can probably make a few safe assumptions based upon the profile of the people you're playing with. I'm sure we all know someone who is a "AAA" member (Any Ace Anytime) player. But even then, you can't be certain. You just have to go with what you do know to baseline your decision, and THEN, after you get to the final percentages, perhaps TWEAK it based upon your "gut" and the players around you.


So, with this in mind, how to determine the number out "outs" you have. A few examples will help illustrate this. Please note, all examples are AFTER THE FLOP, as this article deals with chasing on the flop. A lot of the same concepts apply if you're thinking of chasing after the turn.

FLUSH DRAW. If you're holding 2 suited cards in your hand, and there are 2 of that suit on the board (which happens about 25% of the time), you have the nine (9) remaining suited cards left out there to make a flush, so you have NINE (9) outs. So, remember, "flush draw" = 9.

OPEN ENDED STRAIGHT DRAW. If you have an open ended straight draw, you need either of the cards on the end to make your straight. As there's 4 of each in the deck (times 2), you have EIGHT (8) outs. So, remember, "open ended = 8."

GUTSHOT STRAIGHT DRAW. If you have a gut shot straight draw, you can only fill with 1 card. There are only 4 in the deck, so you have FOUR (4) outs. So, remember, "gut shot = 4."


TWO OVERCARDS TO THE BOARD (NO FLUSH OR STRAIGHT). If you have 2 over cards to the board, you have 3 of each card left in the deck to hit your "overpair", and therefore you have SIX (6). So, remember, "overcards = 6."

TWO PAIR ON FLOP TO FILL A FULL HOUSE. If you flop 2 pair, you have 2 of each of your cards to hit a full house, or FOUR (4) outs. So, remember, "2 pair to full = 4."

PAIR ON THE BOARD. You have 2 outs to hit your "set" and 3 outs to hit "2 pair". Therefore, you have a total of 5 outs. Remember, "pair on the board = 5 outs to improve"

These are some of the most basic situations you can run into. Now, for a more realistic approach, you have to learn how to combine the above, which is where the fun starts.


EXAMPLE 1: 2 Suited overcards and 4 to the flush. To make your flush, you have 9 outs. To hit your overcard for top pair, you have 6 outs. So, 9 + 6 = 15 outs.

EXAMPLE 2: 2 Suited overcards, 4 to the flush, and open ended (about as good as it gets short of having a "made" hand). To make your flush, you have 9 outs. To hit your overcard to the board for top pair, you have 6 outs. To make your straight you have 6 outs. So, you have 9 + 6 + 6 = 21 outs.

I know what you're thinking, "Wait a minute, Professor. You just said it's 8 outs to hit my open ended straight!" You're correct. However, 2 of the cards to hit your open ended straight will ALSO fill your flush. As you've already counted those 2 cards in your 9 "flush" outs, you can't count them again.

POINT TO REMEMBER: When you have a combination of flush and straight draws, you can't count the same cards TWICE. You subtract 2 for an open ended straight, and 1 for a gutshot straight draw.

EXAMPLE 3: A pair on the board (top, bottom, middle) and 4 for the flush. You have 9 outs for a flush, 3 outs to match you kicker, plus 2 outs to make your "set" for a total of 14 outs.

Practice calculating outs and you'll start to see how easy it really is.

PERCENTAGE OF "MAKING" MY HAND – APPLYING THE "RULE OF 4 AND 2"


Once you've managed to get through this mental gymnastics of "HOW MANY OUTS DO I HAVE?", it's time to apply the rule of 4 and 2 to figure out your percentage of making (or improving) your hand.

The "Rule of 4 and 2" is really 2 rules.

The "Rule of 4" is this, "On the flop, multiply the number of outs you have by 4 to determine your chances of catching one of them on the NEXT 2 CARDS."

The "Rule of 2" is this, "On the turn, multiply the number of outs you have by 2 to determine your chances of catching a card on the RIVER to make your hand."


So, looking at our examples above, you have a 60% (4 x 15) chance of filling either top pair or a flush with 2 suited overcards and 4 to the flush on the flop (Ex 1).

You have an 84% (4 x 21) chance of filling either top pair, flush, or straight if you are 2 suited overcards, 4 to the flush, and open ended on the flop.

Lastly, you have a 56% (4 x 14) chance of hitting your set, two pair, or a flush if you have a pair on the board (top, bottom, middle) and 4 for the flush.

PLEASE NOTE that when you apply the "Rule of 2," you may need to recalculate your "outs" for the river card, as often the turn won't make your hand, but give you MORE outs. A classic example is when you "back door" (runner runner) a flush. Example: If you're only 3 to the flush on the flop, and the turn makes you 4 to the flush, you can now add in all the remaining "flush" outs (usually 9) before applying the "Rule of 2."

OTHER USES OF THE "RULE OF 4 AND 2"

The same application of the "Rule of 4 and 2" can also tell you what your chances are to draw out on someone, if you find yourself "All in" and behind.

EXAMPLE 1: A dominated hand or "Counterfeited" hand. You are sharing a card with your opponent who has a higher kicker.

The classic example is sharing Aces. If you have A-5 versus your opponents A-K, you have to hit 1 of the 3 remaining 5's (or get a flop like 2-3-4), so pre-flop, have 3 outs or 9% on the flop to hit. Once the flop comes out, you can then do your normal "Rule of 4" and then the "Rule of 2" to see what your chances are (i.e. a flush draw, straight draw, etcetera). You can also use this to determine the chances of the board pairing up, by applying the same thinking applying 3 outs for each card on the flop. In this situation, 2 pair would result in a split pot.

EXAMPLE 2: Underpair versus Overpair. If you have an underpair to someone's overpair, you have 2 outs, preflop so you have roughly a 8% chance of catching you miracle set. A good rule of thumb is that an over to an under pair is a 4.5 to 1 underdog. Of course, once the flop comes, things change. You might flop 4 to the flush or have a straight draw of some kind, in addition to the "miracle set" example. I once saw pocket Aces lose to pocket Aces when the board was all spades and the turn was the 4th spade for a flush.

WHAT DO THE PERCENTAGES TELL ME?

What do all these percentages mean in terms of whether you should call a bet and chase to making a hand? The short answer is, they tell you HALF of what you need to know, in terms of the math.

The "Rule of 4 and 2" can't tell you if you're chasing to a lower flush than your opponent or if your straight is going to lose to a flush, when the filler on your gutshot makes it 3 hearts on the board. It only tells you if you're going to make SOME KIND of a hand, not necessarily a winning hand. You always have to take into consideration the human element in deciding if it's worth it (your profile on your opponent – is he a rock? Does he bluff a lot? Could he have 2 pair?).


In terms of deciding whether to call or fold, you view the percentages derived from the "Rule of 4 and 2" as the risk or chance you're taking to make a hand. For ease of discussion, we'll call this the "Risk Factor."

Once you know your percentages, you need to figure out what the "Risk Ratio" is. The "Risk Ratio" is an expression of the number of times you'll hit your hand versus the number of time you'll miss, and is noted in the format "TOTAL TIMES YOU PLAY to TOTAL TIMES YOU HIT YOUR CARD." (i.e. "3:1")


To figure out what your "Risk Ratio" is, you need to flip your "Risk Factor" over.

I know, "What the heck does THAT mean?"

Simply put, you have to do some rough division.

EXAMPLE 1: If you have 8 outs (open ended straight draw), you have a 32% chance of hitting on turn / river (Rule of 4). 32% goes into 1, roughly 3 times, so your "Risk Ratio" is 3:1, or you can just remember "opened straight draw is 3:1."


EXAMPLE 2: If you have 9 outs (flush draw), you have a 36% chance of hitting on turn / river (Rule of 4). 36% goes into 1, or (once again) roughly 3 times, so your "Risk Ratio" is 3:1. Alternatively, you can just remember, "flush draw is 3:1."

EXAMPLE 3: If you have 21 outs (open ended, 2 suited overcards with flush draw), you have an 84% chance of hitting on the turn / river (Rule of 4). 84% goes into 1 roughtly 1.25 times, so your "Risk Ratio" is roughly 1:1. Alternatively, you can remember "21 outs is even money."

Now that you have figured out your "Risk Ratio," you need to evaluate you "Risk" versus how much money the pot is giving you. To do this, you need to get comfortable with "Pot Odds."

WHAT ARE POT ODDS?

"Pot Odds" are how much money the pot will give you if you make the call and hit your card.

To use an investment analogy, it's how much money your call (investment) will return on that investment (call).

In a perfect world, you want to invest as little as possible to obtain the biggest return on that investment. If you invest $1 and you get $100 back, you're getting a 100:1 return. If you're investing $50 and getting the same $100, you're only getting a 2:1 return.

To calculate "Pot Odds," you need to count the money already in the pot. This includes the bet made to you (that money belongs to the pot). If you want to get advanced, you can also count the money you expect people behind you to invest into your calculation, but we'll save that discussion for another day.

Once you add up the pot (including bets), you need to figure out the ration of your CALL to the POT.

EXAMPLE: You are heads up and a bet has been made to you. Someone makes a $100 bet into a $300 pot. That's $400 ($300 + $100) in the pot, and it will cost you $100 to win it. $100 to win $400 is 1:4 or (flipped) 4:1 "Pot Odds"

Now, if the pot is giving you 4:1, you would be correct to call THAT bet provided your "Risk Ratio" is LESS THAN THE POT.

If you're holding a flush draw (9 outs), and someone make this bet, you make the call, because your "Risk Ratio" is 3:1 and the "Pot Odds" are 4:1.

Now, I know some smart math person will surely pipe up now and say, "But Professor. 3:1 is actually a HIGHER ratio than 4:1" and they would be correct.

However, who want to sit down and figure out the exact percentages, when all you have to do is remember "if my to 1, is lower than the

So, back to the example: If you have a flush draw (9 outs, 3:1 Risk Ratio) and someone bets $100 into a $300 pot, your "Pot Odds" are 4:1. Since the "Risk" number is lower (3) than the "Pot Odds" number (4), you call.

But what happens if the bet is $300 into a $300 pot? Now, you are getting 2:1 ($300 to win $600). Now, you'd be correct to fold your flush draw (3:1 risk factor) as your "Risk" number is higher (3) than the "Pot" number (3). You might be willing to "gamble it up," since it's such a close number. You might "pay to see another card" and hope you hit. However, if you miss on the turn, a large bet might "price you out" of the pot (making it unprofitable to call).


An please note, that you might STILL fold, even if the "Risk to Pot" ratios is correct, because you suspect your opponent has a HIGHER potential hand he's also running to (i.e. he's drawing to a higher flush draw).

WHY DO YOU MAKE THE CALL WHEN YOUR RISK IS LOWER THAN THE POT?

Simply put, in the long run you'll make more money if you invest more when your risk is lower.

In our above example, if I told you that you would win $400 (4:1 Pot), 1 out of every 3 times (Risk Ratio), you spent $100, you should take that bet. Over the long run, you'll net a win of $400 (the 1 time of 3 you hit – after taking your call out of the pot) and lose $200 (for the 2 in 3 you miss), thus NETTING you $200. THIS IS A GOOD THING.

If the Pot was only giving you 2:1 ($300 bet into a $300 pot), you'd make $600 the 1 out of every 3 hands you won (Risk Ratio), but you'd also $600 (the 2 call in 3 hands you lost, also from the Risk Ratio), netting a ZERO once you subtract your bet (thus the reason you might "gamble it up" or "pay to see the next card.")

If the Pot was giving you LESS than 2/3:1 (a $600 bet into a $300 pot), you'd make $900 on the 1 out of every 3 hands you won (Risk Factor) but, LOSE $1,200 on the hands you miss, NETTING A LOSS OF $300. This is Bad.


Please notice something. The ONLY number which you have ANY control over is the amount the Pot Odds being given to your opponent. You can use this same calculation to figure out how much to bet a good player out of a pot, by making it disadvantageous for your opponent to call in the long run.

For Example: If you put your "pot odds" savvy opponent on a Flush Draw (3:1 Risk Ratio), you would need to bet at LEAST enough to make it less than 3:1 to call. This can be accomplished by pot size or pot size PLUS bet. A pot size bet yields 2:1 pot odds, which makes chasing to a 3:1 flush unprofitable. If your opponent calls, you will make money (and he will lose money) in the long run.

If you bet TWICE the pot ($600 bet into a $300 pot), you opponents should correctly fold his flush draw (3:1), as he's now going to have to bet $600 to win $900 (2/3:1). If he calls, then he's playing a LOSING strategy over the long haul, as he'll win $900 and losing $1,200 in bets (winning 1 in 3 hands and losing 2 in 3 – Risk Ratio).


Got all of that?

I know it seems like a lot, but once you get comfortable with the concept and the common ratios, you'll see it more clearly. If you're 3:1 to hit a flush and your opponent bets less than the pot, you'd be correct to call. The same holds true for an open ended straight draw.

After you call, you have to go through the above exercise on the turn to determine if you should chase to the River.


JUST REMEMBER: IF RISK RATIO NUMBER IS LOWER THAN YOUR POT ODDS NUMBER, IN THE LONG RUN, YOU WOULD BE CORRECT TO CALL AND CHASE.

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ONE LAST THING… A DISCLAIMER

The above analysis and process is intended to be a tool to HELP you make a decision about calling or folding. It is not intended to be a substitute for your own observational skills, hand reading abilities, and intuition. It is intended to show you how you might make PART of the decision which is to say, "Is it worth it for me to consider all the other factors?"

Put another way, whether or not you "hit" your hand does NOT guarantee a win. It doesn't go any good for you to draw to a straight if there's 3 hearts on the board (and you don't have one or you have a low heart). If you flop 4 to the flush and another heart comes on the board, you might be beaten by someone who was also chasing with a single heart in his hand.


Don't say I didn't warn you!

The Professor.