Poker pot odds; all you need to know

Great stuff Mark!! I have always considered whether pot odds was given in European or UK odds. Hence been concerned whether may calculations have been correct when evaluating whether to proceed in flush, straight draw situations.

Interesting stuff, especially the fact that you European’s do things very differently. LOL.

The main thing to keep in mind when calculating odds is that whatever system you use, use it to also calculate your card odds. It would confusing to calculate pot odds using fractional odds but then count card odds using decimal. For example: pot odds of 1:4 ($100 to win $400) while chasing a flush (9 outs with 47 cards left, assuming you have 2 in your hand and 2 on the flop) after the flop would give you 9:38 or approximately 1:4 and not 9:47 or approx. 1:5. When calculating your card odds or OUTS as many call it, you shouldn’t double count your cards. In the above example there are 9 flush cards left (your outs) in the deck (47 cards after 3 on the flop and 2 in your hand) meaning there are 38 cards that don’t help you. Now there could be more cards that help you (top pair, straight) but let’s keep this example as simple as possible to avoid too much confusion. So that leaves you with a 9:38 chance to hit your flush on the turn, or 1:4.22. Had you calculated it the other way you would be double counting your outs, once in our favour and once against you (9:47). I’ve seen people do this and let go of a hand because they thought their odds where not good, when in fact they were getting proper odds to make the call. Hope this helps, if not e-mail me and we can discuss it more.

Hi Mctap

At first I thought you had misunderstood something when you started talking about 9/38 instead of 9/47. After doing some research I now realize you are right, however your comment added to my confusion:-)
The probability of hitting your flush IS 9/47 however the fractional odds against an event are calculated according to the following formula:

Odds = (1-p)/p, where p is the probability

In our example (1-p)/p = (1-(9/47))/(9/47) = (38/47)/(9/47) = 38/9 = 4,22/1

So the probability is 9/47, but the fractional odds are 38/9.
This is why I like using European decimal odds. Here the odds are simply calculated by taking the inverse of the probability.
Hence a probability of 9/47 corresponds to an odds against the event of 47/9 = 5,22.
I will attempt to clarify these issues in my next article.

After reading your response I still find myself confused with the terminology. The point I was trying to get at is that whatever system you use to calculate your pot odds, make sure you use the same to calculate your outs. The problem I often hear is that after calculating their pot odds (4:1 for a $100 bet to win $400) but then use probability to calculate their outs (9 outs with 47 cards left in the deck) instead of fractional (9 cards help and 38 don’t) and this doesn’t work out when deciding whether to call/raise or not. I know after reading my example again, I was a tad confusing in what I was trying to get across.
This just proves that this stuff is confusing at times.

I think the best is the European decimal system as you merely use a calculator to multiply the stakes with the actual odds.

Hi McTap

I hope to clarify the confusions in my next two articles. But you are right when you say that one should stick to the same odds system throughout the calculations.
I do not agree with you when you write “calculate your outs”. Outs are not calculated, they are specific cards that you can count. I think what you mean is that people should use the same odds system in order to calculate the correct expected value (EV) for the hand in question.
This is what I will go into more detail with in my next articles.

Great article and discission thread, one I think that highlights the fact that we all do things a little differently but what is important is that you get to the right answer. Personally, I use percentages… using your flush draw example I always calculate it like so, I have 9 outs, 9 outs after the flop means I am going to hit one of my cards 35% of the time (asssuming I see the turn and the river). I then calculate a few other things like positon in the tournament (I am not a cash player) what percentage of my stack I am risking etc. When calculating the odds of hitting a card that will improve your hand I think it’s handy to have these “outs” numbers at your fingertips, serisoulsy, if you play online you should print out that chart and pin it up beside your monitor. http://casinogambling.about.com/library/weekly/aa050103.htm
If you can’t remember a chart like that or don’t have a printer try to remember that the probability of any given card hitting after the flop is approximatley 2.1%. Multiply that by your number of outs and you have a pretty good estimate of what percentage of the time the next card will imrpove your hand, of course you do the math all over again after the turn and before the river.

Hi JGiles

Thanks for your input! I will elaborate on your “easy to remember rule of thumb” in my next article.

Best Regards

Mark

Cheers to the clear-cut explanation, computation and details. I agree, some poker players, whether just starting or are pros already sometimes need an overview on calculating pots. Good job you’ve done here!

Cheers to the clear-cut explanation, computation and details. I agree, some poker players, whether just starting or are pros already sometimes need an overview on calculating pots. Good job you’ve done here!