Poker Articles About Poker "Odds" including Jan Fisher's Premiere Post

Figuring Odds – Made Easier by Cardplayer’s Jan Fisher

One of the best articles Jan has ever published (her own words and I totally agree with), and eight (maybe twelve now), years after its initial run in Card player Magazine, she still gets compliments and requests to run the “figuring odds” piece again and again. For any player that wants to have a simple method to calculate odds of you making a hand after the flop, read this article. With the authors permission, I present the following and I've presented this in many forums over the years and it's been received so well and I am so proud of my association with her and how great a poker ambassador she is for us all.

It begins:

"This past week I was going through some of the interesting email that I had received lately, and I found a letter that I thought would be of interest to most of you.

Sarah L. from Biloxi, Mississippi, wrote:

“Jan, I have heard and read so much about figuring odds and percentages. Also, much has been written about “outs.” Now, I have been reading your columns and have especially considered the ones in which you cite Mike Caro charts. I have studied and have even mad flash cards, but I can’t seem to memorize the numbers that I think are important. Is there an easy way to calculate outs, chances of getting there, and such? Certainly, there must be a way than flat out memorizing all those numbers. There is, isn’t there?”

The good news in that there is indeed an easier way to figure out the chances of making a given hand without having to memorize long lists of numbers for all the possible hands. It is important to note, though, that this quick and easy method is not 100 percent accurate, although it is close enough to give you a reasonable idea of what your chances are. How close will it get you? To within 1 percent to 2 percent of the exact number you are seeking.

How does it work?

Let us suppose that in hold’em you hold two suited cards in your hand and you flop another two, giving you a four-flush with two cards to come. First, you must determine the number of “outs” that you have – that is, the number of cards left that will make your hand. If you have four to the flush – that is, four of the 13 of your suit – there are nine cards remaining somewhere (either in the deck or in other players’ hands) that will make your hand. Here’s where the trick comes into play. Multiply your “out” cards on the flop (nine) by four. That gives you 36, or 36 percent. So, after the flop, you have about a 36 percent chance of making the flush. The actual number is 34.97 percent, so this easy method has given you a number that’s within 1.03 percentage points of the actual number. That’s fairly close for an answer that came as easily as that. Now, let’s look at the turn card. It’s a blank. Now you still have nine outs, but with only one card to come, you multiply your outs by two and you get 18, or 18 percent. The actual number is 19.57 percent, so you are within 1.57 percentage points of being right on target. As a novice player, don’t these “approximate” numbers give you a lot of information?

Here’s another example to illustrate this gimmick: suppose that you flop a pair. What are the chances that you will make at least three of a kind? You have two outs with two cards to come. Two times four equals eight, so your chances of making trips are about 8 percent. The actual number? 8.42 percent! That’s a pretty good estimate for such an easy task. And with one card to come, multiply that same number of outs (two) by two and you get four, or 4 percent, which is close to the actual number of 4.35 percent.

Play around with these numbers and try some sample calculations to prove to yourself how simple, yet accurate, this method really is. Compare your numbers to the Caro statistical charts found at Mike Caro's own online website, and you will see that the percentages are consistently close for any hand. Remember, with two cards to come, multiply the number of cards that will make your hand by four; with one card to come, multiply by two. It is also important to note that when you figure your outs, there may be other cards that can win for you. For example: if you flop a flush draw and hold A-K, you may want to add the three remaining aces and three remaining kings to count of “out” cards if you think that pairing one of these cards could win the pot for you. There are many things that can be learned with this system, and if you practice when you are not involved in the throes of battle, you will learn to use this tool quickly and effortlessly. "

Class dismissed….Jan Fisher

With permission of Lou Kreiger..

I think you will find this most useful:

Pot Odds Made Easy

by: Lou Krieger©

Because some players have difficulty with the concept of pot odds and others stumble over the practical task of calculating them in the heat of battle, it's time to demystify and sweep out whatever confusion still surrounds this subject while simplifying the arithmetic for readers. In fact, no arithmetic is needed at all. Instead, a handy chart is included that ought to prove helpful to new and experienced players alike.

Figuring pot odds is a necessary part of any poker player's game. Without it, we don't have any way of knowing whether the odds against making our hand are offset by this fundamental relationship: How much will it cost to keep playing this hand and how much money am I likely to win if I catch the card I need? By understanding the relationship between the odds against making our hand and the money we figure to win if we get lucky, we can play skillful high percentage poker instead of treating the game like some form of gambling.

These calculations involve comparing the total number of unknown cards with the number of cards that will complete your hand ¾ the "outs" ¾ then doing a bit of division.
For example, whenever you hold four cards to a nut flush on the turn in a Texas Hold'em game, there are 46 unknown cards, (52 minus your two pocket cards and four on the board). Of those 46 cards, 37 cards won't help you, but those other nine cards are the same suit as your flush draw and any one of them will give you the nut flush.

The odds are 37-to-9, or 4.1-to-1, against making your draw. Percentage poker players will call a bet in this situation only if the pot is four times the size of the bet. In a $20-$40 game, the pot would need to contain at least $160 ¾ or else you'd have to be able to count on winning at least a total of $160 from future calls (this is called "implied odds," and is a guestimate of sorts) ¾ to satisfy this requirement.

If you're the kind of player who's fond of inside straights and other long shot draws, consider this: You have only four outs on the turn. That's not much when you consider that 42 of the remaining cards won't help you at all, and chances of completing your hand are less than nine percent. If you'd prefer expressing that figure in odds, here's the bad news. The odds against completing your inside straight draw are 10.5-to-1, and you'd need a pot that's more than ten times the cost of your call in order to make it worthwhile.

If you had two pair and knew for a fact that your opponent had a flush, you'd be in the same kettle of fish, since only one of four cards will elevate two pair to a full house. When can you play hands like this? On two occasions. The first occurs when you hit the multistate powerball lottery, win 90 million dollars or so, and $20-$40 hold'em now becomes the equivalent of playing for matchsticks. The other occasion is in a game with complete maniacs whose collective motto is: "All bets called, all the time." You would need to win more than 10 times the amount of your call to justify this kind of draw. But if you figure to win a $450 pot by calling a $40 bet with an inside straight draw, go ahead. Go for it.
A chart is provided that makes it easy to learn the odds against all the common draws you're likely to come up against in a hold'em game. If you memorize it, you won't have to waste even a fraction of a second doing arithmetic at the poker table. Personally, I find it tough concentrating on the cards in play and my opponents while trying to do calcs at the poker table. Fortunately, there are simplified methods that allow you to approximate the percentage of time you'll make your hand.

An easy method involves multiplying your outs by two, then adding two to that sum. The result is a rough percentage of the chance that you'll make your hand. Suppose you have a flush draw on the turn. You have nine outs. Nine times 2 equal 18, and 18 plus 2 equals 20. That's pretty close to the 19.6 percent chance you'd come up with if you worked out the answer mathematically.

If you have only four outs, our quick proximate measure (four outs x two, plus two = ten) is very close to the actual figure of 10.5. If you have 15 outs, our quick measure yields a figure of 32, while the mathematically precise figure is 32.6 percent.

The strategic implications of this are simple: If you have a ten percent chance of winning, the cost of your call should not be more than ten percent of the pot's total. With a thirty-two percent chance, you can call a bet up to one-third the size of the pot.

While the "Outs times 2 plus 2" method is an easy calculation to make at the poker table, it's even easier to commit the chart to memory. That way you never have to figure a thing. Just tap into your memory banks and pull out the correct figure. And anytime you find yourself fighting a tinge of self-doubt, you can always double check yourself using the "Outs times 2 plus 2" approximation.

If you want to estimate your chances on the flop without the need for much arithmetic, try this: If you have between one and eight outs, quadruple them. Eight outs multiplied by four yields 32, while the precise answer is 31.5 percent. With four outs, the quadrupling method yields 16 percent, while the accurate answer is 16.5 percent.

With nine outs ¾ a common situation, because it represents the number of outs to a four-flush ¾ quadruple the number of outs and subtract one. You'll be spot-on when you do, since the arithmetical answer is 35 percent. You can use this method up to 12 outs, though with 12 outs our shortcut method yields 47 percent, while the precise answer is only 45 percent.

For 13 through 16 outs, quadruple the number of outs, subtract four, and your results won't be anymore than two percent off dead center. And remember, anytime you find yourself with 14 outs or more, you are an odds-on favorite to make your hand and pot odds of any size become worthwhile.

Note: There is a more defined chart on Lou's own website.

Other Probabilities
Wired Pair: flops a set 11.8 percent of the time

A-K: flops at least one ace or king 32.4 percent

Two Suited Cards: Makes a flush 6.5 percent

Two Suited Cards: Flops a flush 0.8 percent/font

Two Suited Cards: Flops four flush 10.9 percent

Two Unmatched Cards: Flops 2 split pair 2.2 percent

Hanging on to unprofitable draws for whatever reason ¾ and many players persist in drawing to long shots even when they really do know better ¾ can be a major leak in one's game. For many it's the sole reason they are lifelong losing players instead of lifelong winners. There's no real excuse for that kind of play. Even if you are not mathematically inclined (and if you're in this category, you're in the majority. Most people I know loath doing calculations while playing poker) you now have two surefire ways to get the answers without having to do anything more difficult than multiplying by two or four, or memorizing a simple chart. Now all you have to do is count the size of the pot, or even approximate it, compare one to the other, and make your decision. It's that easy. Really.

A final Pot Odds Post from an associate of mine:

Great stuff above, here is another resource, Bill I know and he gave me permission to retype here for you:

Pot Odds – Understanding the Math (Bill Burton Explains)

Many players get confused when the subject turns to pot odds.

Say you have an inside straight draw. Your odds of making that is 10:1

If there is $20 in the pot and it will cost you $5 to call you are only getting 4:1 in pot odds.

If you make that play ten times you will lose nine and win once. The nine times you lose will cost you $45 (9x5).

The one time you win you will win $20

You are minus $25 making this play

Now say there is $60 in the pot and it costs you the same $5 to call. Your age getting 12:1 in pot odds

The odds are still 10:1 against making the draw but this time:

You will lose the same $45 for the nine times that you don’t make it. BUT

You win $60 for the one time you do make it.

You are plus $15.

This is the difference between winning and losing players. If you make the correct play based on pot odds you will be a winner in the long run in a live game because you can always add to your stake at the table

In a tournament however it is different because once you lose your chips you are out. That’s why it is a chip burner to keep making trying drawing hands. You may be getting the correct odds but sometimes you may have to pass if it is a marginal call. (Say you are only getting 11:1 for this play.) Is it worth it if you are short stacked?

Some players think its too much effort to try and keep track of the money in the pot during a live game however when you play online it is right there on the screen in front of you. All you have to do is look ant the money in the pot, the amount it will cost you to call, and you have you odds in an instant. If you are really mathematically challenged you can keep a calculator by your keyboard.

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Bill Burton is a poker book author (Get the Edge at Low Limit Texas Hold'em), and I believe his illustrations in the book are spot on.

Here is a short excerpt from his book on Pot odds:

The Pot Odds is the relationship between the money in the pot and the price of a bet you must make to call. If the pot contains $36 and the size of the bet you must call is $6, we divide the $36 by $6 and we get 6, which means that the pot odds are 6 to 1.

Here is a little experiment that you can try to give you an idea of how the number of players can affect your winning with a hand that has the exact same odds.

This experiment simulates how the number of players will affect a hand that has odds of 3:1 against you. First of all, get a deck of cards and take out the four Aces, twos, threes and fours. You will have 16 cards. Then get coins or chips to use for the experiment.

There will be the four players in the game. Put out a stack of chips out for each player. Each player puts one chip in the pot. Shuffle the 16 cards and deal a card. You can be player number one. Each time an Ace is dealt you win. If a two is dealt then player number two will collect the money in the pot. Likewise if a three or four is dealt the respective player will win the pot. Put another chip in the pot for each player and deal again. Keep repeating this until all 16 cards have been dealt. Notice what the results were.

Each time you win a hand you win three chips. (One from each of the other players)

Each time you lose a hand you lose one chip.

You played 16 hands.

You won four hands and lost 12.

You won 12 chips for the four hands you won and lost 12 chips for the 12 hands you did not win.

You broke even.

The odds of winning were 3 to 1 and the pot odds were 3 to 1.

Now you will repeat the process but player number four will not bet. Anytime four wins put the three chips from the pot (yours and the two other player's chips) aside.

At the end of the 16 hands notice the results:

You won the same four hands. But this time you only won 8 chips.

You lost 12 hands and lost 12 chips.

You are down 4 chips.

Your odds of winning were still 3 to 1, but the pot odds were 2 to 1.

Now put out another stack of chips. This time number four will again play as in the first round and a fifth chip will be put in the pot to simulate an additional player who will not win.

At the end of 16 hands:

You won four hands but this time you won 16 chips.

You lost 12 hands and lost 12 chips.

You won 4 chips.

Your odds of winning were 3 to 1, but you pot odds were 4 to1

With this example you can see how a hand offering the same odds can be profitable when played against a larger field but be unprofitable when you are playing against a limited field.

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After the flop, who is the favorite:







What is the % of times the KQs (all-in on the flop), against the AA will win?

 

You have 13 outs at 4.255% per out = 55.3%

 

((13/45) * (44/44))+((32/45)*(13/44))=0.498 49.8%

 

Rule of 4 and 2, real easy math (if 13 outs) x 4 = approx. 52%, done in a flash.

 

Phil Gordens rule is the best way to go. I was over complicating the matter. Good luck

 

Neither is ahead.

 

the question asked was who is the favorite. over 50% to me would be the right answer for odds , and outs, yet to be the favorite , you would have to have the most outs. aces are ahead, yet a pair of aces have to hit, two aces to win, one ace is bad on the turn or river one spade is bad, one ace a spade, bad, any ace a straight. on the turn or river, so he is minus one out,or two,both aces hitting alone will loose the hand for him, the flop jack spade, ten,heart and two spade. to make full house he has to have runner runner, one ace the other a jack ten or two, or he has to hope the aces hold out, now for outs you have 13 outs with king queen of spades or do you is it not 17 outs, my answer to who is the favorite is simple it is the king queen draw hand,. and also runner runner king or queen also makes this hand a winner, that to me is the probability's of this hand.

 

I agree with David. This is an example where the rule of 2 and 4 doesn't give a very good approximation. Even a calculator like PokerStove or Equilab gives the wrong answer. Is poker a place where you cannot trust anybody or anything? Discuss that.

 

If/Since there's a sizable pot we're entering...the person that has to act last and/or call, essentially is getting a premium for the call. Typically, the person that is forced to call off is at a disadvantage; I don't see this as one of those types of situations.

 

the aces are definitely ahead at this time with only the flop showing,. the turn and river could put them behind with all the outs. the aces have to hold out against the turn and river draw. the favorite is the king queen by virtue of the amount of outs.

 

i guess you need to write a new definition of ahead, and the king and queen are the favorite with 13 outs, if you called the cards with no more draws who would win, leave the flop the way it is and put no more cards out , the winning hand is the pair of pocket aces, at this point and time the high hand is the aces.

 

DRAikens, although the KQ is FAVORITE (it will win more than half the time IF the hand is played out), if the hand were to end right now, the Aces are actually ahead, but nothing is ever decided until someone folds or it goes to the end.

 

that's what i was trying to say,. i just did not agree with no one is ahead idea