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?
