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Message: [QUOTE="SHERMSTICK, post: 458938, member: 7702"] Don't Make These Poker Math Mistakes *** QUESTION FROM A READER *** I am a bit confused on calculating the % chance you will make your hand (the chart you posted on your last newsletter). On the flop you have 4 hearts, and the chance of hitting your hand (flush) on the turn is 19.15%, and the chance of hitting your hand on the river is 19.57%. So, at the point of the flop, isn't your chance of hitting your hand at the end 19.15 + 19.57 = 38.72%? My statistics is a little rusty but I think the math is correct. If this is correct it changes the pot odds to wining odds considerably. Please help me make sense out of this. Thanks, C.B. >>> MY COMMENTS: Great question. It would seem that the odds of making your hand is 38.72%... but that's NOT the case. Also, it would seem that the odds of hitting on EITHER the turn or river would improve your chances, and that you should take that number into consideration... But again, that's NOT how it works. Let's take a deeper look at this, because you've hit on two crucial mistakes that most players make when calculating odds. First, let's bust out our handy chart again. Click here for the web version of the chart: [URL="http://www.texas-holdem-secrets.com/cmd.php?ad=152995"][COLOR=#003399]http://www.Texas-Holdem-Secrets.com/cmd.php?ad=152995[/COLOR][/URL] -------------------------------------------- OUTS TURN RIVER TURN + RIVER 1 2.13% 2.17% 4.26% 2 4.26% 4.35% 8.42% 3 6.38% 6.52% 12.49% 4 8.51% 8.70% 16.47% 5 10.64% 10.87% 20.35% 6 12.77% 13.04% 24.14% 7 14.89% 15.22% 27.84% 8 17.02% 17.39% 31.45% 9 19.15% 19.57% 34.97% 10 21.23% 21.47% 38.39% 11 23.40% 23.91% 41.72% 12 25.53% 26.09% 44.96% 13 27.66% 28.26% 48.10% 14 29.79% 30.43% 51.16% 15 31.91% 32.61% 54.12% 16 34.04% 34.76% 56.98% 17 36.17% 36.96% 59.76% 18 38.30% 39.13% 62.44% 19 40.43% 41.30% 65.03% 20 42.55% 43.48% 67.53% 21 44.68% 45.65% 69.94% -------------------------------------------- This time I've added ANOTHER column to the chart... which is the percentage chance of completing your hand on EITHER the turn OR river, for a given number of outs. Now, you would THINK that if you added the odds of making your hand on the turn, and the odds of making your hand on the river, that it would equal the odds of making it on either the turn or river. Right? I remember thinking this myself... But the TRUTH is, they DO NOT ADD UP. They come CLOSE to adding up, but not quite. Let me give you a really simple example that will show you how this works: Say you take a coin, which has two possibilities: heads or tails. For whatever reason, you want to get a tails. (This is your "out".) When you flip the coin, you have a 50% chance of getting tails. So let's say you're going to flip it TWICE, and you want to know your odds of getting tails at least once. What's the answer? Well, you have a 50% chance of getting tails the first time, and a 50% chance of getting tails the second time. If you add those up, that's 100%. But of course, you know it CAN'T be 100%, because there's a chance you flip heads twice in a row. So what's the deal? This is EXACTLY like poker. The turn card is the first "coin flip" and the river is the second. But you can't just add your chances of making on the turn and then the river... for the same reason you can't add 50% to 50%. Now... the ANSWER to our little puzzle is that your chances of getting tails at least once is 75%. You can break it down like this into four possible outcomes: Flip 1: Heads -> Flip 2: Tails Flip 1: Tails -> Flip 2: Tails Flip 1: Tails -> Flip 2: Heads Flip 1: Heads -> Flip 2: Heads That's all your possibilities. The first three all include a tails, but the fourth does not. So three out of four times you'll get tails: 75%. How do you do this the "mathematical" way? It's actually easy. All you have to do is multiply the chances AGAINST you the first time by the chances AGAINST you the second time. Then subtract that number from one. So... your odds of heads the first time equals 1/2 and your odds the second time equals 1/2. 1/2 x 1/2 = 1/4 Then subtract it from one: 1 - 1/4 = 3/4 And that's it! Don't you just feel SMART right now? OK, so let's tie this back to poker strategy so you can go out and win some more money. Here's what's going to piss you off: The actual percentage number of completing your hand on EITHER the turn or river (the right column in the chart) is practically USELESS. That's right... USELESS! A lot of players think that you should pay attention to the number since it's your "real" chances of making your hand after the flop. The truth is, paying attention to this number is the absolute WRONG thing to do, and will give you very misleading information. Let me explain... OK, so the whole reason you want to know odds and outs is so that you know whether to stay in a hand or not. Let's say you've got A-Q and the flop comes out: J-K-7 That gives you the nut straight draw. But there's only one card that can help you: a ten. Say the action is to you to call a $15 bet. The pot size is currently $60. The "betting odds" are 60:15, which equals 20%. (To get this percentage, divide the bet size by the pot size plus the bet size. In this case it would be 15 divided by 75, which equals 20%.) Anyway... you want to compare these pot odds with your odds of making your hand. You need a ten to make your hand. Let's say you also think that getting a pair of Aces would beat your opponents. There are FOUR tens in the deck, and THREE Aces remaining (you're using one of them), so that gives you SEVEN outs. Using our handy formula for quickly memorizing odds, you double seven and add one. So you've got a 15% chance of making your hand. Based on this information, you should FOLD. You'd be getting bad odds on your money (15% versus 20%). Now... what if you used the percentage chance of making your hand on EITHER the turn or river? How would that change things? Well, the percentage chance of making your hand on the turn or river with seven outs is 27.84%... Which is HIGHER than 20%... Which means you should CALL, right? WRONG. The reason is this: IF YOU USE THE TOTAL PERCENTAGE NUMBER, YOU'D HAVE TO COMPARE IT WITH THE TOTAL BETS AND POT SIZES. Here's what I mean: Let's say you call the $15 bet from our example. The turn card comes out and it's a five. This doesn't help you at all. Now the action is to you AGAIN... this time to call a $25 bet with a pot size of $100. AND THAT IS WHY YOU ALWAYS CALCULATE ODDS BASED ON ONE CARD, NOT TWO. The reason is you must ANTICIPATE the NEXT bet. Odds should be taken into consideration for EACH BET, which means they must be calculated PER CARD. The $25 bet means you're getting 20% on your money (25/125) which is once again too high for the 15% odds on your hand. The reason you can't try to calculate the betting odds for both the turn and river in ADVANCE is because you just don't know what the bet after the turn will be. And here's the kicker... USUALLY the bet after the turn is much HIGHER than the bet after the flop... especially if your opponent has a hand. This means you get a poor return on your money. OK... so we've covered WHY the turn card percentage plus river card percentage does NOT equal the total percentage. And we've discussed why you should NOT look at the total percentage when comparing it with your bet sizes. Now let's briefly look at a question about outs... *** QUESTION FROM A READER *** Down toward the end of these tips, you mention other players holding some of the cards. Shouldn't that be considered everytime you're figuring the odds and based on the number of players in the game? For example: If you're waiting on a flush draw, you have two and there are two showing, but there are five players besides you; Doesn't that lower your outs and how much should that be considered or what percentage should be deducted? Thanks R.H. >>> MY COMMENTS: Yes, you are absolutely correct. The problem with odds is that you can only calculate them accurately when the conditions are just right. If there are five players in a hand and you're on the flush draw, then YES, you should expect some of the same suit to be in someone else's hands. This is especially true with cards like Aces. If you're at an 8-man table and four players see the flop, there's a good chance at least one or two of them are holding an Ace. So if you need an Ace, you've got to take this "guess" into consideration. The key to remember is that odds calculations are just one tool in your toolbox. If you find yourself in a situation where you can't do the math, then DON'T. Go with your gut and use the countless OTHER poker strategies to win the hand. *** QUESTION FROM A READER *** Hey Roy, in your two flush draw examples, you didn't consider hitting a straight with 2 running cards on the turn and river... why not? How would you include that in your odds calculation? Thanks for all the good education so far. R.F. >>> MY COMMENTS: I hardly ever do runner-runner calculations when thinking about odds... And the REASON is because the actual percentage is too minuscule to matter. It's almost always less than 1%. Anyone at the card table who stays in a hand in hopes of catching a runner-runner straight is what we call a... FISH! Period. Don't be one of these suckers. Just stick with the core formulas and calculations I've taught you... The knowledge of pot odds, counting outs, and understanding poker math will give you a DEFINITE EDGE over your competition... >>>>>>>>Roy SHERMSTICK:cool: [/QUOTE]

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