[Closed] What is the chance of....

"Full house flops"/"All possible flops"*100% = 18/19,600*100 = 0,09%

Not sure if it's right tho ♦

Formula Explanation:

[(A)/(B)]*C = Total Flop Combinations

A = Total Permutations of Flop Cards
B = Denominator to get base combinations. It is the factorial of the number of times you've taken from the same "pool" of cards, look at quads calculation as its the easiest to grasp.
C = Used When there is more than one possible way to get the hand (One card paired or the other, etc.)

Permutations are the total number of possible flops where every different order of cards is counted as separate i.e. A :spade:Q :heart:5 and 5 :diamond:A :spade:Q are both counted. We use B to eliminate this so that all possible permutations of three specific flop cards are counted as one.

Flop Combinations:

Flops that do not improve hand:

(44*43*42)/(1*2*3) = 13244 possible flop combinations

Flops with one pair:

[(6*44*43)/(1*1*2)] = 5676 possible flop combinations

Flops with two pair:

(3*3*44) = 396 possible flop combinations

Flops with just a set:

[(3*2*44)/(1*2)]*2 = 264 possible flop combinations

Flops with a Full House:

[(3*2*3)/(1*2)]*2 = 18 possible flop combinations

Flops with Quads:

[(3*2*1)/(1*2*3)]*2 = 2 possible flop combinations

Total Odds:

Pair or Better:Everything Worse

6356:13244 = 1:2.1

Two Pair or Better:Everything Worse

680:18920 = 1:27.8

Set or Better:Everything Worse

284:19316 = 1:68

Full House or Better:Everything Worse

20:19580 = 1:979

Quads:Everything Worse

2:19598 = 1:9799

Hope this helps, if you have any questions just reply here so everyone can benefit from the explanation.