[scottwire]

The main problem is this:

Now, again correctly speaking, of those 16 cards out-of-play, the expected number of Spade 's is 1 in 4, or the expected number of Spade 's left is actually 5, not 9 which gives you only a 5 in 30 chance of drawing a Spade or 16.7% which is 3 percentage points less of a chance to draw a flush.

If 16 cards are out of play of 46

You want

9/46 = x/16


16*9 = 46x

144 = 46x

x = 3.13 cards out of those 16 in people's hands will be spades

Not 1 in 4 like you said

[KYBill]

Originally Posted by d_p

OK, this has been bugging me for some time. (I'm sure this is not anything new and it has been discussed to death a million times.) Is there a flaw in the way we are told to calculate outs?

Let's say you are playing THE against 8 other players. You have:
in the hole
and the board is:
.

How many outs do you have?

Conventionally we are told that we have 9 's left in the deck and there are 46 unseen cards, so you have a 19.6% chance of drawing a spade. So we need pot odds of about 4 to 1 to make a correct call.

Welllll..... it can be argued yes and no. Correctly speaking there are 46 unseen cards and there are 9 spades left among those cards.

BUT 16 of those 46 cards are either in-play or have been mucked. (Another three have also been burnt, but I won't go into that just yet.) That means there are only 30 cards that have not been dealt.

Now, again correctly speaking, of those 16 cards out-of-play, the expected number of 's is 1 in 4, or the expected number of 's left is actually 5, not 9 which gives you only a 5 in 30 chance of drawing a or 16.7% which is 3 percentage points less of a chance to draw a flush.

OK, now let's get back to the burn. Your expected number of spades in the three burn cards is .75. Now you only have 4.25 in 27 cards or a 15.7% chance to draw a flush on the river. That's 4 percentage points less than the "conventional" way we are told to calculate outs. In other words, your chance of drawing a has been reduced by 20% following this logic and you actually need 5 to 1 pot odds to make a correct call.


What think? How has this line of reasoning been de-bunked?

What are you smoking? Dont try and out think yourself.

[2_hotty]

Originally Posted by d_p

16 of those cards have zero chance of being dealt to you. If the cards are in fact randomly distributed as you say, there are 4 's among them meaning you have zero chance of getting those 4 's.

Absolutely wrong.

There is no way of knowing if 4 of them are spades so you can't count them out.

Look at what you know. You know that you hold 2 's. You also know that there are two 's on the board. And you know that there are 13 's total in the deck. This leaves you with 9 possible 's you could hit to make your flush.

Base your calculations on what you know.

[d_p]

OK OK OK... on my long drive home tonight I discovered the error in my ways. I was wrong to assume that the chances of the 16 dealt/mucked cards being a was 1 in 4. It is actually.... (drum roll please).... 9 in 46. doh!

SO, looking back at your replies, it looks like only two of you actually correctly pointed out the error in my ways.

Sorry for wasting your time and for polluting the Net with the stench of my brain fart.

[d_p]

Originally Posted by 2_hotty

Absolutely wrong.

There is no way of knowing if 4 of them are spades so you can't count them out.

Look at what you know. You know that you hold 2 's. You also know that there are two 's on the board. And you know that there are 13 's total in the deck. This leaves you with 9 possible 's you could hit to make your flush.

Base your calculations on what you know.

Your results are correct, but your thinking is not. YES, I CAN count out the spades in the 16 dealt/mucked cards. But as I discovered when I was thinking more clearly (ie: thinking while not at work lol) and as scottwire correctly pointed out, the chance of the 16 and the chance of the other 30 having spades are identical, so whether you count them out or not, the result is the same.

[d_p]

Originally Posted by KYBill

What are you smoking? Dont try and out think yourself.

What was I smoking??? Clearly it was the fumes from my brain farts!

[Captn_All_In]

Originally Posted by d_p

OK, this has been bugging me for some time. (I'm sure this is not anything new and it has been discussed to death a million times.) Is there a flaw in the way we are told to calculate outs?

Let's say you are playing THE against 8 other players. You have:
in the hole
and the board is:
.

How many outs do you have?

Conventionally we are told that we have 9 's left in the deck and there are 46 unseen cards, so you have a 19.6% chance of drawing a spade. So we need pot odds of about 4 to 1 to make a correct call.

Welllll..... it can be argued yes and no. Correctly speaking there are 46 unseen cards and there are 9 spades left among those cards.

BUT 16 of those 46 cards are either in-play or have been mucked. (Another three have also been burnt, but I won't go into that just yet.) That means there are only 30 cards that have not been dealt.

Now, again correctly speaking, of those 16 cards out-of-play, the expected number of 's is 1 in 4, or the expected number of 's left is actually 5, not 9 which gives you only a 5 in 30 chance of drawing a or 16.7% which is 3 percentage points less of a chance to draw a flush.

OK, now let's get back to the burn. Your expected number of spades in the three burn cards is .75. Now you only have 4.25 in 27 cards or a 15.7% chance to draw a flush on the river. That's 4 percentage points less than the "conventional" way we are told to calculate outs. In other words, your chance of drawing a has been reduced by 20% following this logic and you actually need 5 to 1 pot odds to make a correct call.


What think? How has this line of reasoning been de-bunked?

Oh GOD......head.....hurting......bad...........




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oh god......I puked on my shoes.......

[SpeakEasy]

Glad we cleared that up.