Figuring Odds - Made Easier by Cardplayer's Jan Fisher
One of the best articles Jan has published (her own words and I totally agree with), and eight 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. 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 www.caro.com, 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