Quick Pot Odds Calculating

[Tottenham]

Sitting in live home games, I can obviously get a quick percentage on hand odds, but pot odds seem to give me more difficulties. I know the theory, but getting that math through the head in a reasonable time is often challenging.

Anyone have any tips or tricks to make these calculations under time pressure? Obviously if it's nice round numbers (ie: 20 bucks in, 5 bucks to you for a call), there is no problem, but often this is not the case.

[Molinero]

Sitting in live home games, I can obviously get a quick percentage on hand odds, but pot odds seem to give me more difficulties. I know the theory, but getting that math through the head in a reasonable time is often challenging.

Anyone have any tips or tricks to make these calculations under time pressure? Obviously if it's nice round numbers (ie: 20 bucks in, 5 bucks to you for a call), there is no problem, but often this is not the case.

Took the words right out of my mouth!

There's a reason I don't teach math...and it's that I suck at it.

[RiverMonkey]

I can't find the other posts where these were mentioned. It's kinda nice to have them all in one place anyways.

There are a number of 'tricks' you can use for making immediate/effective pot odds based decisions. (If you are looking for help on doing quick division or multiplication of two numbers, all I can suggest is to round off to the nearest whole number.)

p = pot odds = current (or effective) pot size/amount to call
n = number of unseen cards = 47 on flop, 46 on turn
o = number of clean and/or partial and/or hidden outs

'Backwards Method':
I like this one best for at the table ...

if o*(p+1) > n you should call

or, p*o > n-o

I call this next one the "rule of 13" (think I got this one from KoolMoe):

This one only works if you have 5 through 9 outs.

If 5<=o<=9, then: 13 - o

is your approximate odds-against for hitting on the next card, then compare that to p.

"Rule of 4-2"
This one is for people who like to work with probabilities rather than odds-against .... I personally don't like using it during the game, but it can be useful otherwise.

With two cards to come, o * 4 is your approximate probability (P) of hitting by the river

With one card to come o * 2 is your approximate probability (P) of hitting on the river card.

(Do the actual calculations for 1 <= o <= 25 using the exact formulae for two and one card to come respectively, and plot the actual probability against the number of outs and also plot the linear lines P=o*2, and P=o*4 and you'll be able to visually see the range of outs for which the rule of 2-4 needs to be corrected (don't confuse p with P ... p is pot odds, and P is the probability of hitting a card with one or two to come).

Krieger's Modified Rule of 4-2
This one takes the above method, and corrects the approximate results for specific ranges of o.

2 cards to come:

if o=1 thru 8, then P=o*4
if o=9 thru 12, then P=(o*4)-1
if o=13thru 16, then P=(o*4)-4

1 card to come:

if o<5, (o*2)+bit
if 5<=o<=9, (o*2)+1
if o>9, (o*2)+2

Regardless of which method you use, this is the easy part. Believe it or not, figuring out a good value for your number of outs is probably the hard part. You need to consider so many subtle possibilities including hidden outs, partial/discounted outs, re-draws, back-door draws, possibly drawing dead, etc. etc.

Lastly, remember to give yourself some foregiveness is you fall short on pot odds alone, but it's close. Implied odds may come to your rescue if you hit.

[Tottenham]

p = pot odds = current (or effective) pot size/amount to call
n = number of unseen cards = 47 on flop, 46 on turn
o = number of clean and/or partial and/or hidden outs

'Backwards Method':
I like this one best for at the table ...

if o*(p+1) > n you should call

or, p*o > n-o

Im confused with the above.

Very simplifed example: $20 pot, $5 to you to call.

You are 4 to a flush after flop.

Using the above: o=9, n=47, p=4
9*(4+1) = 45 isnt greater than 47, so fold
or
4*9 is not greater than 47-9 so fold

Now, comparing this to my original way of thinking through the above.

pot odds: 20/5 = 4 - You need to win this hand 1 in 5 times to break even, or 20% of the time.

hand odds: 9 outs = 1.86 to 1 - You will win this hand once in approx 3 times played, or approx 34% by the river.

By the above calculations, this would be a call. Where did I go wrong?

[Molinero]

That was great stuff!

Is it possible (read: likely) that we could make Rivermonkey's above post a sticky? That's very helpful stuff.

Anyone? Anyone? Bueller?

[RiverMonkey]

Im confused with the above.
.....

By the above calculations, this would be a call. Where did I go wrong?

Technically, p in those equations is the effective pot odds so you need to consider future action in the hand not just what the pot is immediately offering. If you are only considering taking the flush draw to the turn and no further then you can't use 1.86:1. You'd have to use 4.22:1 which is the odds of hitting the flush on the turn card.

See my responses in the following thread for a more detailed explaination:

http://www.flopturnriver.com/phpBB2/...pic.php?t=7593