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Thursday, October 20, 2005 

What are the odds?

A few days ago I was watching a hand play out on the 10/20 hold’em game at The BBC. Several players were in the hand, and there was some considerable pre-flop action. When the flop came, the guy who was first to act bet a large amount, prompting the next guy to take a while to think about his move. I made a comment saying “hey, if you have a flush draw (it was showing on the board), you have about 18% chance of hitting it.”

As soon as I made a comment, a couple of players in the game immediately “corrected” me saying “No, its 38%.” I responded by saying that I was only talking about hitting it on the turn, and not both turn and river. They then said “ No, it’s 38% on the turn, and about 8% on the river” or something like that. I didn’t want to argue anymore so I just shrugged and didn’t make any more comments. It’s hard to argue with someone who thinks they are right, and I believe most of us in our small community would like to think that we DO know what we are talking about when it comes to poker.

I’d like to think that most of us (including me) are in some ways still pretty damn clueless when it comes to the science of poker. Im gonna post something i learned from a poker newsletter i get on email about calculating odds and i hope it helps everyone understand poker odds better.

Say 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%. (these are mathematically correct odds) So, at the point of the flop, isn't your chance of hitting your hand at the end 19.15 + 19.57 = 38.72%

Most of us think this way, that we should add the percentages of the turn AND the river and base our decisions from those odds, but that actually should NOT be the case! It is actually a very crucial mistake that's gonna cost you in the long run! In the math point of view, they DO NOT add up, although it is relatively close.

Here is a very good and easy to understand example of how it works.

Say you take a coin and you want to get tails for some reason. Now you know your odds of getting tails is 50% (heads or tails are the only possibilities). Now let's say you want to know your odds of getting tails if you flip it TWICE. You have a 50% chance of getting it the first time, and a 50% chance of getting it the second time right? So does that means you have a 100% chance of getting tails? of course not, since you have the possibility of getting heads TWICE, right?

This is exactly like in poker, the turn card being the first "coin flip" and the river card being the second. You dont just add up the chances of making the turn and the river for the same reason that you cant add 50% to 50%.

Now the answer to the coin flip question is that your chances of getting tails at least once is 75%. You an break it down into four possible outcomes:

1st flip: heads/ 2nd flip: tails
1st flip: tails/ 2nd flip: tails
1st flip: tails/ 2nd flip: heads
1st flip: heads/ 2nd flip: heads

So those are the possibilities, 3 out of four times you will get tails, which is 75%. Taking this into consideration, we can now see that computing your odds for BOTH turn and river and basing you action on this CAN cost you a lot of pots. Why? because it just shows that computing for odds on BOTH will make it appear that your chances are better than they actually are. Another thing is if you use BOTH and total them, you are comparing them againt the current pot size thus giving you WRONG pot odds. to put it more simply, you will be making a decision to call when the odds are, in reality, AGAINST YOU.

ALWAYS calculate odds based on one card, and not two for the simple reason that you must anticipate the next bet. Why will you calculate your betting odds for BOTH turn and river in advance when you DONT know what the bet after the turn will be? makes sense doesn't it?

Just remember, always base your calculations on one card, and not two.

and another thing, NEVER EVER calculate runner-runner odds simply because the percentage is so small that it is insignificant (less than one percent). anyone on a table who chases a runner-runner draw is what we call DEAD MONEY.

These are just a few points that can be learned and is available out there to anybody who takes the time to look it up and research about it. We can all do our share in improving the whole poker community by learning about things like this and sharing the information to other players.

Remember, the better everyone gets, the more we all improve as a whole.

that makes sense. it's really something i have to think about.
thanks for the inputs.

hey dude... i dreamt about you and german snake last night. for some reason kumakanta daw kayo habang nagbo-bowling. di ba musical ang dating?

haha anak ng tipaklong ang labo nun ah.

Check out this site... http://www.expss.com/poker/probab.htm

oh, 5th line from the vert bottom...

anonymous posted a site saying you have a 39% chance of "winning" when you are drawing for a flush.

i repeat, basing your bets on these kinds of calculations is a losing proposition. If you read the post, and understood it, it would have made perfect sense.

you have a "39%" chance of HITTING (not winning the hand) your flush (again, the math is wrong because he added BOTH percentages), and so you compute your odds based on the pot in front of you (before the turn or river) and comparing it with the odds of hitting UNTIL THE RIVER. Using those percentages can be very misleading.

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 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 150 bet. The
pot size is currently 600.

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. 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.

Odds should be taken into consideration for EACH BET, which means they must be calculated PER CARD.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.

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  • The best poker I've ever played has always entailed peace. A relaxed comfort. Eyes open, ears open, radar up. Absorbing my opponent's every message. Taking them as they come. Not mixing what those messages are with what I want them to be. It's like an aerial view. A view from above the myriad luck-dependent reactions of those many people who never gain such a peace. And when you gain that view, that peace - when you'd rather have the truth, no matter how disappointing, over a false hope, no matter how desirable - then you're a player. The hand you're on slips into a stream of thousands of other hands, no one of which, because of your lofty view, seems unduly important, no false fearful emotions rise within you. When you gain the peace of lofty perspective, you're a player, and when you're a player, you're free.- from "King of a Small World" by Rick Benett
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