Formula for calculating pot odds?

[rod johnson]

I found this formula on a poker website.

A = The number of cards in the deck that will improve your hand.
B = The amount of money (in dollars) in the pot.
C = The maximum amount of money (in dollars) that you have the correct pot odds to call in order to see another card.

( [ ( A * 2 ) + 2 ] * 0.01 ) * B = C

Is this correct, or is it some boneheaded attempt to calculate pot odds?

[Richard Berg]

It's a pretty poor approximation, and even then it (1) only works when the number of cards removed from the deck is small (i.e. only in flop games) (2) doesn't account for cards that improve your hand but do not give you the nuts. Here's a quick table of odds with 46 unknown cards, for reference:

<font class="small">Code:</font><hr /><pre>
outs real odds your formula
1 46.0 25.0
2 22.5 16.7
3 14.7 12.5
4 10.8 10.0
5 8.4 8.3
6 6.8 7.1
7 5.7 6.3
8 4.9 5.6
9 4.2 5.0
10 3.7 4.5
11 3.3 4.2
12 2.9 3.8
13 2.6 3.6
14 2.3 3.3
15 2.1 3.1
16 1.9 2.9
17 1.8 2.8
18 1.6 2.6
19 1.4 2.5
20 1.4 2.4
21 1.2 2.3
22 1.1 2.2
</pre><hr />

Even the old "subtract your outs from 13" trick is better, IMO. If you're playing limit hold'em, you only need to memorize the first 8 or so.

[rod johnson]

It was posted specifically for hold'em. If it's bunk, then what would be the correct formula (if there is one) for calculating your pot odds in hold'em?

Using an example hand:

$50 NLHE cash game.
.50 / $1 blinds

Stacks:
BB has $35 in chips
UTG+2 has $75 in chips
Our Hero has $127 in chips

Say you’re on the button with
A /images/graemlins/diamond.gif10 /images/graemlins/diamond.gif
UTG+2 raises it to $5, you call, the SB folds, and the BB calls. This creates a pot of $15.50. Now, the flop comes:

9 /images/graemlins/spade.gif8 /images/graemlins/diamond.gifJ /images/graemlins/diamond.gif
The BB checks it and UTG+2 bets $20, creating a $35.50 pot.

At this point you have 17 outs to improve your hand to either: a Jack-high straight, a Queen-high straight, or the nut flush (I am not counting an Ace as an out because a likely hand you could be facing is AJ). How would one calculate the pot odds of this situation? Is there a formula to do this?

[gronmo]

Calculating pot odds is quite easy. Just compare how much money you have to put into the pot versus the chance you have of improving to the winning hand.

In this situation you got 15 outs (not 17, you got 9 diamonds and 3 8's and 3 Q's) giving you a chance to improve of (15/47)*100 = 31.9%

The amount you have to call compared to the pot is
(20/(35.5+20))*100 = 36.0%

Since your chance of improving is lower than the amount you have to call its usually a fold here. You also need to consider your opponents possible hands here. The BB has yet to act and could reraise 35 (all-in) which could cause the preflop raiser to also go all in to isolate himself with the BB. In such a situation you cannot possible call a raise.

[driller]

What about the implied odds?

[driller]

Since you're a favorite (0.8:1) to hit by the river with 15 outs, why wouldn't you just go all in?

[gronmo]

Well you need to consider the fact that if you make your hand it might not be the nuts. Your opponents could have 88 99 TT JJ or an overpair. So a Q or 7 could mean a split pot. Any 8 9 or J could also give someone a full house or quads. An overcard could also give someone a redraw.

Since this is a 50$ buy in and you have accumulated 127$ I think its better to fold the hand here and instead get your money in when you actually have an advantage.

[rod johnson]

[ QUOTE ]
In this situation you got 15 outs (not 17, you got 9 diamonds and 3 8's and 3 Q's) giving you a chance to improve of (15/47)*100 = 31.9%

[/ QUOTE ]

Dude, your answers are so screwed up...
8's pair the board and are anything BUT outs in this situation!
Your outs are:
4 - 7's
4 - Q's (not three!)
9 - diamonds
17

&lt;jeez!&gt; I could've have gotten "help" like this on RGP!!!

[CORed]

If you count 4 7's and 4 Q's, you are counting the 7/images/graemlins/diamond.gif and Q/images/graemlins/diamond.gif twice. 15 is correct.

[rod johnson]

D'oh!

You're right, of course.

[driller]

3:2 dog against a set and q high straight(unlikely), 5.5:4.5 dog against j high straight (even more unlikely). Favorite against everything else (two handed), including AA, KK, and QQ.

It is a gamble. But then again he might fold.

[pudley4]

[ QUOTE ]
[ QUOTE ]
In this situation you got 15 outs (not 17, you got 9 diamonds and 3 8's and 3 Q's) giving you a chance to improve of (15/47)*100 = 31.9%

[/ QUOTE ]

Dude, your answers are so screwed up...
8's pair the board and are anything BUT outs in this situation!
Your outs are:
4 - 7's
4 - Q's (not three!)
9 - diamonds
17

&lt;jeez!&gt; I could've have gotten "help" like this on RGP!!!

[/ QUOTE ]

I think we all understood he had a typo when he said the 8's were outs. His answer is correct. Your correction is wrong, and you were an ass about it. Think before you type.

[rod johnson]

[ QUOTE ]
I think we all understood he had a typo when he said the 8's were outs.

[/ QUOTE ]
Then surely you all understand that it was a typo when I said, "&lt;jeez!&gt; I could've have gotten "help" like this on RGP!!!"

What I meant to say was, "&lt;jeez!&gt; I couldn't have gotten help like this on RGP!!!"

Also, considering Richard Berg's post saying that this formula would only work with "flop games"... Uhh, yeah! I posted this in the "Texas Hold'em" forum.

You 2+2 guys are just too darned smart for me. /images/graemlins/wink.gif

Honestly though, grono's post just confused me (due to the typo). CORed's post pointed out my out-counting error for me, and helped me to realize that grono's math was correct. Berg's post was basically irrelevant to my question.

I'll go back to RGP now and leave you 'superior thinkers' alone.

[SossMan]

[ QUOTE ]
I'll go back to RGP now and leave you 'superior thinkers' alone.


[/ QUOTE ]

You could take "superior" out of that sentence. it's superfluous.

[rod johnson]

[ QUOTE ]
You could take "superior" out of that sentence. it's superfluous.

[/ QUOTE ]

They warned me that you 2+2 guys were condescending, haughty, and arrogant... boy were they wrong!

Forget about RGP. I'm gonna fit in just fine around this place, now that I understand the 'process' of attempting to learn something from 2+2'ers.

1) Ask a question.
2) Weed through error-ridden and erroneous answers.
3) Withstand juvenile name-calling for pointing out error-ridden and erroneous answers.
4) Get 60% of your original question answered.
5) Gain final acceptance as one of the "2+2 A-Holes".

WooHoo! I'm in, boys!!!

[rod johnson]

I hope it isn't a problem for me to post again so soon after my previous post. I'm still learning the ropes here at 2+2, the pinnacle of poker thought and discussion.

If it's not too much trouble, could one of you Mensa members answer my original question (from the beginning of this thread)?

Is this formula accurate for calculating pot odds?

A = The number of cards in the deck that will improve your hand.
B = The amount of money (in dollars) in the pot.
C = The maximum amount of money (in dollars) that you have the correct pot odds to call in order to see another card.

( [ ( A * 2 ) + 2 ] * 0.01 ) * B = C

Based on my own analysis it is very accurate when you have a large number of outs on the flop, but there is some deviation when the number of outs is small (4).



Oh, I'll save some time, and just go ahead and call myself an "ignorant jackass, who is not worthy of your lofty answers, but begs for your counsel on bended knee. I prostrate myself before thee, O' Gods of mathematics and forum etiquette!!! Amen."

[SossMan]

What part of this did you not understand?

Calculating pot odds is quite easy. Just compare how much money you have to put into the pot versus the chance you have of improving to the winning hand.


The chance you have to improve the hand is simply:
A = your # of outs
B = unseen cards

A/(B-A) = % chance of improving your hand on the next card.

It seems like you already knew that, though.

[driller]

I think a method that is simple and accurate is: divide the number of cards to come by the number of outs and subtract one. This gives you the correct odds (to one) against hitting your out with one card. Example: After the flop (47 cards to come)you determine you have 9 outs. (say to hit a flush draw). Divide 47 by 9 = 5.22 minus one = 4.22. Divide the amount currently in the pot by the amount of the bet you have to call. Compare the two numbers. If the second number is bigger, you have the odds to call the bet. In the example above anything more than $12 in the pot would justify calling a $3 bet. As you can tell by the answers to your original question, it is hardly ever that simple a decision.

Using your equation and $13 for the amount of the pot, I get $2.60 as the break even amount you could call, which is too low -- again using only current pot odds and no other considerations.

[rod johnson]

I understand your exlpanation, and I see how you are thinking of it terms that can be used at the table. Thanks for the thoughtful reply!

Wouldn't you add the UTG+2 player's $20 bet into the pot amount before figuring the pot odds though?

[rod johnson]

[ QUOTE ]
[snipped first 4/5th of asinine diatribe]...It seems like you already knew that, though.

[/ QUOTE ]

Uhh, yeah. I did. That's probably why I didn't ask that.

I know I'm not worthy of your attention, but I have to ask at this point; why the hell do you keep replying to me without answering the damned question which I am asking?

I guess I'm just not smart enough to understand a subtle move like that... Damn you 2+2 guys are smooth! /images/graemlins/smirk.gif

[driller]

Correct. In the hand you posted you add the $20 UTG+2 bet to the pot to create the $35.50 pot. My example was not related to the hand you posted. If you only use the 15 outs with one card to come method I used you would get 2.13:1 against hitting one of the outs vs 1.78:1 pot odds so on those considerations alone you wouldn't call.

But if you knew he had aj, you should call because you are a favorite to win the hand. Actually you should go all in. But just on the one card outs vs pot odds, you should not call.

[rod johnson]

Understood.

Yeah, it's another subject entirely to disucuss the implied odds and strategies for that situtation. I just needed an example hand in order to illustrate my question.

[driller]

Hey, good luck and welcome. I just went from stranger to newbie to journeyman myself. This is a good place, believe me, but if you drop the dude bomb on someone, you need a thick skin. Just learn.

[Richard Berg]

[ QUOTE ]
Berg's post was basically irrelevant to my question.


[/ QUOTE ]
Did you miss the whole frickin' chart showing how your formula diverged from the actual values?

Welcome to the forums, BTW /images/graemlins/tongue.gif