What is the possibility of this actually happening?
Bottom line: shit happens.
Quote: gosport42No doubt I'm just really curious as to what the math behind this happening would be.
It difficult to say with any certainty. There are a number of parameters which must be specified (players to the flop, players seeing the river, would all hands be shown down, etc.)
Also coincidences like this are often more common than we initialy believe and when calculating odds that is often not taken into account. Examples:
-This would still be noteworthy if it happened in hands one apart
-This would still be noteworthy at any point in the night
-This would still be noteworthy if the hands happened in the reverse order
-This would still be noteworthy if it was quad 10s instead of 9s or SF to the 10 instead of 7
All this is to say I think what you want to know is more like:
"What are the odds that we would have back to back hands of quads or better in a 12 handed game over 200 hands?"
Is that right?
Quote: gosport42So last night I was at a home NL hold em cash game. A few more people showed up than as expected and as a result we were playing 12 handed..... so right of the bat the chances of getting anything spectacular will be cut. well about an hour into the game a guy gets a four of kind, where three nines were on the board and the fourth was in his hand... when this happened I was a little shocked as I figured I probably wouldn't see anything greater than a full house all night. well it gets better.... the very next hand the person sitting to his left gets a straight flush 3-7. So my question is: What is the probability that with 12 players playing, those two hands come up consecutively?
More players doesn't reduce the odds of 4 oaks and above. In fact, it'll increase them, as you have 12 possible hands in each round, not 10.
Quote: endermikeIt difficult to say with any certainty. There are a number of parameters which must be specified (players to the flop, players seeing the river, would all hands be shown down, etc.)
Also coincidences like this are often more common than we initialy believe and when calculating odds that is often not taken into account. Examples:
-This would still be noteworthy if it happened in hands one apart
-This would still be noteworthy at any point in the night
-This would still be noteworthy if the hands happened in the reverse order
-This would still be noteworthy if it was quad 10s instead of 9s or SF to the 10 instead of 7
All this is to say I think what you want to know is more like:
"What are the odds that we would have back to back hands of quads or better in a 12 handed game over 200 hands?"
Is that right?
Pretty much basically
Quote: thecesspitMore players doesn't reduce the odds of 4 oaks and above. In fact, it'll increase them, as you have 12 possible hands in each round, not 10.
In some cases yes, but having dealt out 24 cards at the beggining as opposed to 20 cards is going to make it that much harder to find outs would it not?
Quote: gosport42In some cases yes, but having dealt out 24 cards at the beggining as opposed to 20 cards is going to make it that much harder to find outs would it not?
If you have 5 cards in your hand, and 5 card for the flop/turn/river, there are 42 cards left that won't be played.
If those 42 cards are in 1 pile of 42, do the probabilities change?
If those 42 cards are in 42 piles of 1, do the probabilities change?
If those 42 cards are divided into 8 - 5 card hands with 2 left over...
Quote: gosport42So last night I was at a home NL hold em cash game. A few more people showed up than as expected and as a result we were playing 12 handed..... so right of the bat the chances of getting anything spectacular will be cut.
how on earth did you get this idea?
Quote: gosport42In some cases yes, but having dealt out 24 cards at the beggining as opposed to 20 cards is going to make it that much harder to find outs would it not?
It would not.
No.Quote: gosport42In some cases yes, but having dealt out 24 cards at the beggining as opposed to 20 cards is going to make it that much harder to find outs would it not?
Unless you know someone is holding or has folded one of you outs, then it's still part of the total of all the unseen cards, and has as much of a chance of hitting the board as any card in the stub.
(Based on 1,000,000 rounds)
Since each hand is independent (assuming good shuffling) we can then spitball that out of 200 hands we would expect about 4 hands to qualify. Again taking each hand as independent we can guess that on about 8% of nights you would see a back to back of quads or better in a 12 handed game (200 hands per night).
We can do other stuff like find the chances of it happening with other gaps like 3 hands apart, but for now I'm going to leave it at that unless someone has a particular extension they desire. This is mostly because I do not like the 2% figure. I would definitely try to improve that, because there is probably more error there than in all my other approximations combined.
There are many possible embellishments to get a better number that 2%:
-First would folding non-promising hands along the way (probably very important).
-Second would be pulling out any times the board make it to quads or better without help (probably unimportant).
(edited to show code properly, thanks miplet)
------------------------------------------
function out = TH(reps)
results = zeros(reps,1);
%{
results(r) = result of round r
0=no big hand
1=straight flush
2=royal flush
3=quads, pocket pair
4=quads, 1 card in hand
5=quads, all on board
%}
for r = 1:reps
deck = randperm(52);
board = deck(1:5);
boardMat = zeros(13,4);
for k=1:5
i = mod(board(k), 13)+1;
j = ceil(board(k)/13);
boardMat(i,j) = 1;
end
if max(sum(boardMat))>=3 %check for SF
boardMat;
for k=1:12
ihole1 = mod(deck(2*k-1+5), 13)+1;
jhole1 = ceil(deck(2*k-1+5)/13);
ihole2 = mod(deck(2*k+5), 13)+1;
jhole2 = ceil(deck(2*k+5)/13);
tempMat = boardMat;
tempMat(ihole1,jhole1)=1;
tempMat(ihole2,jhole2)=1;
for s=1:4
for d=1:9
if (sum(tempMat(d:d+4,s))==5)
tempMat;
results(r)=1;
end
end
if (sum(tempMat(10:13,s))==4)&&tempMat(1,s)
results(r)=2;
tempMat;
end
end
end
end
if max(sum(boardMat,2))>=2 %check for Quads
boardMat;
for k=1:12
ihole1 = mod(deck(2*k-1+5), 13)+1;
jhole1 = ceil(deck(2*k-1+5)/13);
ihole2 = mod(deck(2*k+5), 13)+1;
jhole2 = ceil(deck(2*k+5)/13);
tempMat = boardMat;
tempMat(ihole1,jhole1)=1;
tempMat(ihole2,jhole2)=1;
for d=1:13
if (sum(tempMat(d,:))==4)
results(r)=sum(boardMat(d,:))+1;
tempMat;
end
end
end
end
end
ind = find(results);
out = [ind, results(ind)];
-----------------------------------------------------------------
With an execution statement of:
tic, reps = 1000000, out = TH(reps); length(out)/reps, toc
------------------------------------------------------------------
And output of:
reps =
1000000
ans =
0.0208
Elapsed time is 411.377902 seconds.
From the 1,000,000 runs I see about 84% or the big hands come from quads. So I delved a bit deeper. Around 2/3rds of those quads come from having only 1 of the 4 in the quad in the hole. (The other 33% are essentially pocket pairs since board almost never quads by itself.) Clearly a lot of those would be tossed unless there was some high cards value in all but the most loose of games.
I would say my original number is an upper bound, and a loose one at that. I would readjust it to 4% of nights and still call that a "not tight" upper bound.
Quote: endermikeCode if you care (Matlab):
(sadly the site seems to not want to preserve the indentations: sad. It looks so much clearer indented properly)
Just use put code in like this:
[code]
code goes here
[/code]
