Poker Odds Should Be Calculated On One Card , Not Two : ...

[Kramer]

POKER ODDS SHOULD BE CALCULATED ON
ONE CARD NOT TWO

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.


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.


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%
--------------------------------------------

look at
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.

The pot is $ 60 , + $ 15 / $ 15 = 5 or 20%
You have 7 outs +1 = 8
15% on turn or river .
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.

[The Fan]

good read, thanx kramer

[The Loner]

It is very difficult to calculate the exact odds of hitting a drawing hand when you're sitting at the poker table. Unless you're a genius with a gift for mathematics like Chris Ferguson, you will not be able to do it. That leaves two options for the rest of us: The first option is to sit at home with a calculator, figure out the odds for every possible combination of draws, and then memorize them. That way, no matter what situation comes up, you always know the odds. But for those of us without a perfect memory, there's an easier way. Here is a simple trick for estimating those odds.

The first thing you need to do is to figure out how many "outs" you have. An "out" is any card that gives you a made hand. To do this, simply count the number of cards available that give the hand you are drawing to. For example: suppose you hold Ac 8c and the flop comes Qh 9c 4c. You have a flush draw. There are thirteen clubs in the deck and you are looking at four of them -- the two in your hand, and the two on the board. That leaves nine clubs left in the deck, and two chances to hit one.

The trick to figuring out the approximate percentage chance of hitting the flush is to multiply your outs times the number of chances to hit it. In this case that would be nine outs multiplied by two chances, or eighteen. Then take that number, multiply times two, and add a percentage sign. The approximate percentage of the time you will make the flush is 36%. (The exact percentage is 34.97%.) Now let's say that on that same flop you hold the Jd Th. In this case you would have an open ended straight draw with eight outs to hit the straight (four kings and four eights). Eight outs with two cards to come gives you sixteen outs. Multiply times two and you will hit the straight approximately 32% (31.46% exactly) of the time.

One important thing to keep in mind is that the percentage stated is merely the percentage of the time that you will hit the hand you are drawing to, NOT the percentage of time that you will win the pot. You may hit your hand and still lose. In the first example, the Qc will pair the board and may give some article a full house. In the second example both the Kc and the 8c will put a possible flush on the board, giving you the straight, but not necessarily the winning hand. Still, knowing the approximate likelihood of making your hand is a good beginning step on the road to better poker.

[The Loner]

kramer---thanks for the information---did you write this too?

[Kramer]

For example: suppose you hold Ac 8c and the flop comes Qh 9c 4c. You have a flush draw. There are thirteen clubs in the deck and you are looking at four of them -- the two in your hand, and the two on the board. That leaves nine clubs left in the deck, and two chances to hit one.

The trick to figuring out the approximate percentage chance of hitting the flush is to multiply your outs times the number of chances to hit it. In this case that would be nine outs multiplied by two chances, or eighteen. Then take that number, multiply times two, and add a percentage sign. The approximate percentage of the time you will make the flush is 36%. (The exact percentage is 34.97%.) Now let's say that on that same flop you hold the Jd Th. In this case you would have an open ended straight draw with eight outs to hit the straight (four kings and four eights). Eight outs with two cards to come gives you sixteen outs. Multiply times two and you will hit the straight approximately 32% (31.46% exactly) of the time.

This example is fine when you hold an ace high club

what about a King Club?

Your opponent could have Ace club flush draw ,
Pair of queens ,
2pair q,9...

now your outs are discounted by the Ace that can beat you ...

the situation has totally changed ...