how to calculate your odds fast on Flop

[freeman]

I published this table in my blog (sorry if you cannot read Chinese). On flop, there are two cards to come, assume you are going to the river and all the 47 cards are unknow to you, you have N outs, then the accurate percentage you win is AcuP=100x[1- ((47-N)/47)x((46-N)/46)]. it is not an easy work to complete the calculation in your mind in a moment. However, I got a easy way to do it in just 1 second. My approximate formula is

EstP= 4xN - r

where r is:
0 for N<9,
1 for N=9, and
N-9 for N>9.

In the table, first column is number of outs, 2nd column is the AcuP, 3rd column is the EstP, and the next untitled column is the difference. you can see that they fit very well, all within 1% for N<20. but it is very rare that N>20.

In the Green Area, I give some modification for 46 and 45 unknow cards. In case you have very good guess on your opponent's one or two cards, or in casino some cards are accidently exposed, then you accually have 46 or 45 unknow cards. The listed number are the real probability, you can see that it is easy to memrize them: if you know one card(46 unknow), then add 1 to EstP, if you know 2 cards, then add 2 to EstP.

[tesla_styx]

Cool estimation! thanks for sharing.

[DblDownTrent]

is it possible to be behind on the flop and have 20+ outs? haven't really thought about it that much, but am curious.

TdJd vs 2c2s on a 8d9d9c board?


any 7,8,T,J,Q, any diamond.

[Judge Dredd]

Originally Posted by DblDownTrent

is it possible to be behind on the flop and have 20+ outs? haven't really thought about it that much, but am curious.

TdJd vs 2c2s on a 8d9d9c board?


any 7,8,T,J,Q, any diamond.

if you have 20 outs, 40 of the 45 cards are yours.

[hardinda]

After the turn change it to 2xN-r ... good to go for your final card. I usually use N with 8 instead of 9. Apoc pointed this out awhile back I think.

[Sotally Tober]

Originally Posted by Judge Dredd

if you have 20 outs, 40 of the 45 cards are yours.

[hardinda]

DDT ... (4x20) - (20-9) = 69% ... so, that answer is NO

[Arachn]

Actually 45 unknown is very useful - Omaha

[win diesel]

I'm pretty fooking dumb. I need to play better. But why not just use the rule of 4 (flop) and 2 (turn)?

[Judge Dredd]

Originally Posted by win diesel

I'm pretty fooking dumb. I need to play better. But why not just use the rule of 4 (flop) and 2 (turn)?

thats good enough win. There is no need to get it down to the 0.000X% precision unless you have xray vision and know exactly what your opponent(s) hold.