I'm interested in questions like what % of hands contain A2 or how many flops have 2 low cards without a deuce. For plo8 and 5 card if possible. I haven't been able to find this info. Do I need to learn that pro poker tools query language or is there a resource for this?

Thanks

Do you have an excel spreadsheet? For questions of this nature, you will find that is the best way to go. Combin(x,y) will be your new best fried.

How many hands contain A2?
AAA2 = combin(4,3) * 4
222A = same as AAA2
AA22 = combin(4,2) * combin(4,2)
AA2X = combin(4,2) * 4 * 44
A22X = same as AA2X
A2XX = 4 * 4 * combin(44,2)

Your denominator here will be combin(52,4)

How many flops have at least 2 distinct low cards?
Three distinct ranks = 4* 4 * 4 * combin(8,3)
Two Distinct Ranks plus a high card = 4 * 4 * 44 * combin(8,2)
Two of same rank plus another low card = combin(4,2) * 4 * combin(8,2)

Your denominator here will be combin(52,3)

Once you understand these principles you can answer almost any question in the same fashion.

Again, RIP Buzz.

Awesome, franknagaijr. Let me just add that at least in OpenOffice it's combin(x;y).

i'll add

your browser's address bar can substitute for a spreadsheet(atleast true for both chrome and firefox)
4 choose 2 will get you the same answer as excel combin(4,2).
52 choose 4 will get you the same answer as excel combin(52,4)
etc.

Its been a while. Here is a little more to amuse myself.

If you have A2HH in hand and only care about the other six ranks
LLL (distinct) = c(24,1) * c(20,1) * c(16,1)
LLH (distinct) = c(24,1) * c(20,1) * c(18,1)
LLL (one pair on board) = (c(4,2) * 6) + c(20,1)

Since you know your own hand, the flop denominator is c(48,3)

I got a little bit of the math wrong in my original response, fwiw.

i believe the LLL (distinct) and LLH (distinct) equations fail to take into account that the order of the cards does not matter.

so if
LLL (distinct) = c(24,1) * c(20,1) * c(16,1) / c(48,3)
= 24 *20 *16 / 17296
= 7680 / 17296
= 44.4%

7680 fails to incorporate that the order of the cards doesn't matter.
to remove the order of the cards it needs to be divided by 6 because there are 6 ways the same 3 distinct ranks can be ordered and be the same flop.

(7680/6)/17296 = 7.4% which is correct

LLH (distinct) = (24*20/2 *18) /17296 =24.97% is correct




LLL (one pair on board) = (c(4,2) * 6) + c(20,1) =4.16% which is correct

Good stuff ngFTW, and sounds right too. I haven't run any numbers in this fashion for half a decade or more I'm sure.

ZockenRobot - If you search my hella old posts, you may find plenty more examples of this kind of math.

My answer is

I toyed with excel for several hours and learned a thing or two, at least on how to use excel. Highly recommended.

some assistance (for reference as you amuse yourself)

when holding A2HH ie. A2KQ

there are 38 distinct flop textures when considering the ranks as either low cards (Ace thru 8) and high cards (9 thru king) as well as the flops intersection with the hand

flop quads
LLL ie. AAA,222 2/17296 =.01%
HHH ie. KKK,QQQ 2/17296 =.01%

flop boat
LLL ie. AA2,22A 18/17296 =0.1%
LLH ie. AAK,AAQ,22K,22Q 36/17296 =0.21%
LHH ie. AKK,2KK,AQQ,2QQ 36/17296 =0.21%
HHH ie. KKQ,KQQ 18/17296 =0.1%

flop set
LLL ie. AA[3-8],22[3-8] 144/17296 =0.83%
LLH ie. AA[j-9],22[j-9] 72/17296 =0.42%
LHH ie. [3-8]KK,[3-8]QQ 144/17296 =0.83%
HHH ie. KK[j-9],QQ[j-9] 72/17296 =0.42%

flop 2pr
LLL ie. A2[3-8] 216/17296 = 1.25%
LLH ie. A2K,A2Q 54/17296 = 0.31%
LLH ie. AK[3-8],AQ[3-8],2K[3-8],2Q[3-8] 864/17296 = 5.0%
LLH ie. A2[j-9] 108/17296 = 0.62%
LHH ie. AKQ,2KQ 54/17296 = 0.31%
LHH ie. AK[j-9],AQ[j-9],2K[j-9],2Q[j-9] 432/17296 = 2.5%
LHH ie. [3-8]KQ 216/17296 = 1.25%
HHH ie. KQ[j-9] 108/17296 = 0.62%

flop 1 pr. paired flop
LLL ie. A[33-88],2[33-88] 216/17296 = 1.25%
LLH ie. [33-88]K,[33-88]Q 216/17296 = 1.25%
LHH ie.A[jj-99],2[jj-99] 108/17296 = 0.62%
HHH ie.K[jj-99],Q[jj-99] 108/17296 = 0.62%

flop 1 pr. unpaired flop
LLL ie. A[3-8][3-8],2[3-8][3-8] 1440/17296 = 8.33%
LLH ie. [3-8][3-8]K,[3-8][3-8]Q 1440/17296 = 8.33%
LLH ie. A[3-8][j-9],2[3-8][j-9] 1728/17296 = 10%
LHH ie. [3-8][j-9]K,[3-8][j-9]Q 1728/17296 = 10%
LHH ie. A[j-9][j-9],2[j-9][j-9] 288/17296 = 1.66%
HHH ie. K[j-9][j-9],Q[j-9][j-9] 288/17296 = 1.66%

flop nothing trips flop
LLL ie. 333-888 24/17296 = 0.14%
HHH ie. 999-jjj 12/17296 = 0.07%

flop nothing paired flop
LLL ie. [3-8][33-88] 720/17296 = 4.16%
LLH ie. [33-88][j-9] 432/17296 = 2.5%
LHH ie. [3-8][jj-99] 432/17296 = 2.5%
HHH ie. [j-9][jj-99] 144/17296 = 0.83%

flop nothing unpaired flop
LLL ie. [3-8][3-8][3-8] 1280/17296 = 7.4%
LLH ie. [3-8][3-8][j-9] 2880/17296 = 16.65%
LHH ie. [3-8][j-9][j-9] 1152/17296 = 6.66%
HHH ie. [j-9][j-9][j-9] 64/17296 = 0.37%

17296/17296 =100%


(annoyingly there is no tab to help with formatting and not inspired to make edit it into table. sorry)

confirmed correct

That's fantastic ngFTW!