Calculation of an odd - Help

[ScanX]

Hi,

I read in Lee Jones book that once you've flopped four to a flush, you are a 1.9:1 dog to make it by the river and if you flop an open end straight flush draw, you are a 1.2:1 favourite to make a straight or better by the river.

I don't understand how these calculations are made.

Any help appreciated.

Thanx in advance

ScanX

[Dave B]

Someone else will give a more precise answer than me...but here goes. If you are one card from a flush w/ the turn and river to come you have 9 outs (each remaining card of your suite). Each out has about a 2% chance of hitting, so on the turn and river you have roughly a 18% chance of hitting with each card, so a 36% chance of hitting. The odds are then in inverse of that-so roughly 2:1.

W/ a open end str8 flush, you have the 9 outs from the flush and 6 more from the str8 (open end str8 has 8 outs, but 2 will be the same as the flush draw). So w/ 15 outs, times 2%=30% or so. 2 draws, around a 60% chance of hitting the str8 or the flush.

[packerfanr]

basically, for any odd-calculating:

you need to figure out how many "outs" you have. How many cards, still in the deck, would give you the desired hand. Example- open ended straight draw- you have cards 5-8....you need a 4 or a 9....well think, theres 4 4's and 4 9's left unshown. That is 8 "outs". You take that number and make a fraction with it and the total number of cards left in the deck.

So, 8 outs and 47 cards left (3 on the flop and 2 in your hand, subtract that from 52 and its 47) the fraction is 8/47.

But there is still 2 cards left to come

On the turn, you have a 8/47 chance, but on the river, assuming you didnt get the card, you now have a 8/46 chance.

Add 8/47 and 8/46 and you have your answer.

That is the basic way to figure out all odds.

[HalfSugar]

packerfanr, I'm a big fan of that explanation, that's the simplest I've ever heard it and I've tried to explain it a million times and never managed it that well

Kudos to Dave B too who is perhaps the most useful guy on the forum right now

[Adamm]

I think I'm actually starting to enjoy explaining odds.
Here we go with the most exact way to do it.
The flush draw on the flop. You've got 9 outs, and 47 unseen cards on the turn, 46 unseens on the river. To account for the fact that you could potentially hit your card twice, you have to invert the outs and subtract from 1 later on. So your chance of NOT hitting it would be 39 outs and 38 outs on the turn and river. The math would end up being...
1-[(39X38)/(47X46)]
Which comes out to about .35 or 35%
Convert then to Lee Jones speak with poker formula [(100/ x%)-1] and compare that to 1, so 100/35 -1 is 1.86 to 1 against.

BTW, wasn't there some argument on this forum somewhere about how to convert probabilities or percents to the x to 1 format? There it is.

The flush draw is the same thing but plug in different outs. That can be somebody's assignment to post that.

[packerfanr]

for a quick estimate...here is what i recomend...take your outs, multiply that by how many cards are left to show up, and multiply that by two.

Example..you have 8 outs to get a straight..this is off the flop...take 8 (outs) multiplied by 2 (cards left to come(turn, river)) and then double it....about 32%

I find it will usually be within 2 percent of the correct number. However, I am not sure on the accuracy. If anyone can come up with a time where it is wrong..please inform me.

(i also posted this in the odds and probability section but felt it was appropriate here)

[JimTheBullet]

Whilst I agree with all of what has been said on this thread about odds there is one consideration that nobody has mentioned that needs to be taken into account. Unless the player who made the bet (and any others still in the hand) is all in, you should not be thinking about the probability of making your hand by the river, you should only think about the probability of making it on the next card. This is because if he bet on the flop and the turn brought no obvious out for you then he is likely to bet again forcing a recalculation of odds.

For example, using simplified odds, say you have four to a flush on the flop and an opponent bets, the odds of you making the flush on the turn are about 4/1 (9 outs 47 unknown cards). If the pot, at this point, offers you something near that then you should think about calling it. However, if the turn card is a blank then your opponent will surely bet again forcing you to consider the odds of hitting the flush on the river.

I think it is foolish to say to yourself "I have an xx% chance of making this hand by the river" because you will be using the wrong odds in your comparison of pot odds v out odds.