Weird Odds

[Rocko4]

Hi everyone, I'm new here, 19 years old.

To my knowledge, to calculate the probability of hitting, you taking your # of outs, multiply by 2 and add 1. Where things get hazy is when I picture an entire deck of cards, and I plan to turn over 1 card; I want to calculate the probability of it being a heart. We all know its 25%, but according to the formula, since theres 13 hearts (outs), I would take 13, multiply by 2, and add 1, which would get me 27, or 27%, as opposed to 25%. Can someone clarify this for me?

Thanks in advance, and look forward to chattin about poker with all of you.

[Skribbles]

Were did you get your X2 +1 theory?

[kellerumd]

try using this instead. you have two hearts, there are two hearts on the board, that makes nine left in the deck. you take the numer of cards left in the deck that would help you 9(13 in a deck, minus the 4 hearts you alredy see) divided by 47 (52 minus your hand and the board). Remeber, if this is on the flop you have two chances to catch this card too.

Also, on a somewhat unethical note, if you are in a home game, keep track of flashed cards, like the bottom of the deck and what not. that could change your decision.

[DougisRad]

No offense, but your knowledge is wrong. This equation you have, whoever told it to you, has no idea what he or she is talking about.

Here's how you do it:

52 cards in a deck, you want the probability of flipping over a heart. 13 hearts, SO, you have 39 bad cards and 13 good cards, which is 39:13 odds, or 3:1 odds.

Now, to make an odd a probability, you must do this: The odds are X:Y, so [Y/(X+Y]x100%

Therefore, [1/4]x100% = [.25]x100% = 25%

[Iron Butt]

Zowie. No offense intended either Doug, but I believe y'all are both wrong. OK I'll take a shot.

The "rule of four" is a well known method of roughly figuring odds as a percentage post-flop, which is simply outs x 4, which is roughly your odds to hit if you stay to the river. From the turn (4th board card) it's x 2 or I've seen 2x + 1 also, I usually just stick with x 2. Outs are counted based on all known cards, so if we need hearts, and we're holding two and two are on the board, we have 9 outs, not 13.

For an example, let's say we have a flush draw on the flop. You have Ah 2h in your hand, and there are two hearts on the board. This leaves 9 hearts, x 4 is 36% or about 2 to 1 against. From the turn, it's x 2 = 18, plus 1 because you have the same amount of outs but there's one less card left (again, we are deriving a very rough estimate here), for about 4 to 1 against.

In practice it's usually a bit more complicated. For instance it's common to have dead outs, the most common example would probably be if you have a straight draw with a possible flush on the board, say: You: Kd Qs, Board: Jh Th 2c. You'd have to give up 2 outs if you put an opponent on the flush draw, since the Ah or 9h makes the flush.

[DougisRad]

No offense taken. Also, please don't take offense to this: You didn't read his post thoroughly. He said in the whole deck, the odds of turning over 1 heart.

I know what's more important are the odds in an actual hand, but that's not what he asked. :D

[HalfSugar]

No-one wants to be sat at a table doing 13/47 and stuff like that so the quick and dirty 'four-two' rule is fine by me

[Rocko4]

ok, I am a little bit more confused now. I got my formula from this site http://www.pokertips.org/strategy/strategy.php .

[Iron Butt]

OK, I admit to trying to get right to what I saw as the point.

From pokertips.org:
To calculate your percentage of hitting an out on the next card, you take the # of outs times 2, then add 1. In the above situation with 8 outs, you have roughly a 17% chance of hitting on the turn.

This is correct: outs x2 + 1 for the odds of hitting the NEXT CARD. Roughly. Over a span of two cards i.e. from flop to river it's roughly twice that. Why? Because each out card represents a 1/47 chance or a little over 2%. Why 47 rather than 52? Because you know your 2 cards, plus 3 more cards on the flop, total 5 known cards, and being known they must be subtracted from the total. Why does your 52 card example come out 27% rather than 25? Because the rule of 4 is for 47 cards (slightly over 2%) rather than 52 (slightly under 2%). Note that you are still within 2%; this is about as good as the rule of 4 gets, as noted it's for deriving a rough estimate, and most people find it close enough.

What do you find confusing?

[Rocko4]

what I find confusing is if you take that formula and apply it to a whole deck of cards by saying 'what is the probability that the next card (first card flipped over) is a heart?'

According to the formula, it would be 13 outs, multiplied by 2, and then to that we add 1. This gives us (13 x 2) + 1, which equals 27, or 27%... the answer, as we know is 25%, so the formula doesnt agree with the above situation.

[Loonbat]

what I find confusing is if you take that formula and apply it to a whole deck of cards by saying 'what is the probability that the next card (first card flipped over) is a heart?'

According to the formula, it would be 13 outs, multiplied by 2, and then to that we add 1. This gives us (13 x 2) + 1, which equals 27, or 27%... the answer, as we know is 25%, so the formula doesnt agree with the above situation.

This formula is not used on a full deck of cards. This formula is used (the 2/4 rule basically) looking at the odds to hit by the river, whether the current situation is you're looking at the flop or you've seen the turn. It's a good approx., which is good enough for most pot odds calculations.

[Nut Flush]

Keep in mind that formula isn't supposed to be perfect. It's used to give you a quick estimate, not an exact figure.

[Iron Butt]

Yup... didn't I say this stuff already? :D

To recap your 52 card example doesn't work out because the rule of 4 is for 47 cards not 52, 47 cards being 52 - 2 (for your hand) - 3 (for the flop), which is the situation where people are usually trying to calculate odds in hold 'em. The only time there is 52 cards in the deck is before the hand has started. And also as stated the rule is for a rough approximation anyway; it will not give you a mathematically exact answer; it will usually be a few percent off, but much better than guessing or being oblivious.

Good luck. Don't feel bad if you don't get this stuff right away, no one's born knowing how to play poker. :D

[Rocko4]

I understand now.. thanks guys!