Quote:
Originally Posted by All-inMcLovin
Tyvm!
Great thread!
I saw some website with a ton of math saying that straight flush over straight flush in general was about 1 in 5 million iirc.
So your math seems correct to me.
Had this discussion with a math PhD at the table recently, but briefly:
What is more likely, quads over quads OR straight flush over quads?
He said intuitively that straight flush over quads seemed more likely to him. I thought for like a minute and suggested that quads over quads instead was more likely.
Thanks again bip!!
I am pretty sure quads over quads wins more BBJ and of course is more likely.. but let's work out the math.
I will just do it as a heads up game to simplify the math, and the relationship of relative likeliness will hold even with a full table.
So first we are looking for specific boards.
For quads-quads we need XXYYZ (where X, Y, and Z represent ranks).
There are 52*51*50*49*48 / 5! ordered boards = 2,598,960 different boards.
Of those, you have 6 combos of XX, 6 combos of YY, and 13 * 12 / 2 combos of XXYY, and 44 leftover cards (that do not make trips on the board) for Z = 6 * 6 * 13 * 12 / 2 * 44 = 123,552 "double paired" boards.
So the likeliness of getting a double quad eligible board is (123,552 / 2,598,960 ~= 1/21. Hmm.. seems more likely to get a double paired board than I would have guessed. Although I guess we often do not make the river in a hand, so we would not have an accurate perception of this. Another shortcut to solving this problem is just "how likely is 2 pair in 5 card stud"... which seems about right at 1/21.
Ok - so now you need two opponents to have two exact holdings to get the BBJ. I will work this as a heads up problem just to simplify - as it should give us a concept of what is significantly more likely (quads v quads or quads v SF).
Two villains could have [47*46/2 * 45*44/2] / 2 orders of hole card combos = 535,095 possibilities. Exactly ONE = 1 of these possibilities fulfills the BBJ.
So to have quads vs quads BBJ eligible in a heads up match would be:
1 / 535,095 * 123,552 / 2,598,960 = 1 in 11,255,912.5
Before you say "wow, how does it ever happen".. That is for a heads up match. It is much more likely 9~10 handed.
(Part two in next post - odds of SF vs quads)