A very quick way to derive pre-flop odds (feedback appreciated)

[aaaaa]

Hi,

The very useful 2-and-4s rule comes about by linearising the expression 1-(1-x/47)*(1-x/46)

Is there some way, *pre-flop* odds can be derived?
I am interested in FLOP and FULL-BOARD situations.

I gave it a try. Please check/advise.

PART A ---
For FLOP: outs x 4 + 8
For FULL: outs x 4 + 26

This fits well.
PART B ---
How to remember which are blank? flop = 3, and full = 5. Use the table of 6 for the top three flop blanks and the table of 7 for top five full_board blanks)

thanks

[Orlando Salazar]

There are simulators and odds tables that give approximate preflop odds. Not that these matter but sooooooo much. Also, add 4-5% for everyone that folds b4 u.

[jay_shark]

You may use a least squares approximation method and find the line that best fits .If I have some time I may try to work this out but it looks like your approximation is not bad .

[aaaaa]

@ salazar: Are you allowed to take a calculator to a casino?
@ jay: yes but how are you going to do --
12* 3.35 + 5.23 in your head?
isn't 12*4+8 much cleaner?

I tried regression first.
but in a regression fit, if there are one or two outliers.. that will severely affect the accuracy of the table. but if there IS an easier to remember fit, please post!

[Orlando Salazar]

Lol, memorize the chart. You should be able to add increments of 4 or 5. Just know pocket pairs increase in value the more short handed you are.

[jay_shark]

easy 12(3+1/3) + 5 +1/4 = 36+4+5+1/4=45.25 :P

I suppose you want a linear equation with integral coefficients .

You may also get an upper bound the following way .

3x/47=~3x/50=~ 6x/100. This comes from P(AuBuC)=pA +pB +pC -pAB -pAC-pBC +p(ABC) .
a denotes flop card 1
b denotes flop card 2 etc

The intersection of events is about x/47*x/47*3 ~2*3*x/100*2x/100 ~ 12x^2/10000 =~1/10x^2/100 .

So an approximate probability for 6 outs is 6*6/100-1/10*6^2/100 = 36%-3.6%=32.4%

for x=10 this is 6*10/100 - 1/10*10^2/100 = 50%

[aaaaa]

@ SALAZAR: whats your source on this? Could you direct me to a link please?

@ Jay: Yes I know the approximation 1/47~2%... that is how we get the 2and4 rule... 1-(1-x/47) ~ x/47 ~x*2%.
Could you explain why the intersection is x/47*x/47*3

Also guys, what is a good thread on 2+2 with practical outs information? Calculation comes easy to me, would i'd like to capitalise on that skill.

Thanks much

[KipBond]

[ QUOTE ]
For FLOP: outs x 4 + 8
For FULL: outs x 4 + 26

[/ QUOTE ]

I'm confused. The 2/4 rule estimates the odds of you hitting your outs. So, you are doing the same thing pre-flop, right? It's ~2% per card. So FULL would be outs * 10. Or am I misunderstanding what you are saying? I think I am, because how do you count your outs pre-flop?

[jay_shark]

You may have f1f2 f1f3 or f2f3 . There is also a third intersection but we can disregard since we are approximating anyway and the probability of this happening is low .

That is , you may have two of your outs appear on flop card one and flop card two . Or , you may have your card appear on flop card one and flop three etc . So x/50*x/50 is the probability card 1 and card 2 contain your outs . So we have to multiply this by three since there are three ways to pick two cards from three .

[Ace_to_Bass]

In the linear regression test you deemed innacurate, try running the same test choosing the option to 'Ignore Outliers'....that should work best.