Questions re: Probability of Higher Flush by WoO

luvvly jubbly.

Even allowing for a bit of divergence as x and y increase, my figures are never more than 0.8% out from yours.

So..back to my original question 1:- What is Mr Wizard doing to get his figures?

Oddly ("ODDly" haha!), if I regenerate my numbers post-flop (i.e. divide by combin(47,2)= 1081), I get identical results to the Wizard, but (as before) displaced by one column.

(If only I knew how to paste tables into this thread....)

And the other question, of course, is "is this method generic enough to be applied across other scenarios?"

e.g. if i can calculate the heads-up (i.e. 1 opponent or 2 total players) probability of the other player having a better hand, can I then infer the probabilities for 2, 3....n other players?

Muchas Gracias for the input on this miplet!

Sorry for the late arrival.

To answer the question at hand, I don't remember how I came up with that table. My attempts to recreate those numbers have failed. So I think I made a mistake somewhere.

I just updated my table with the way I should have done it. If c is the number of overcards and p is the number of total players, including yourself, then the answer should been:

1-(1-(COMBIN(8,2)-if(c<=6:combin(8-c,2),0))/COMBIN(45,2))^(n-1)

As I noted, this is just an estimate. I would take Miplet's simulation results over my estimate.

Speaking of which, I ammended my answer to include your table Miplet. I hope that is okay. If you prefer another attribution other than "miplet," please let me know.

Quote: Wizard

Sorry for the late arrival.

To answer the question at hand, I don't remember how I came up with that table. My attempts to recreate those numbers have failed. So I think I made a mistake somewhere.

I just updated my table with the way I should have done it. If c is the number of overcards and p is the number of total players, including yourself, then the answer should been:

1-(1-(combin(8,2)-if(c<=6:combin(8-c,2),0)))/combin(45,2))^(n-1)

As I noted, this is just an estimate. I would take Miplet's simulation results over my estimate.

Speaking of which, I ammended my answer to include your table Miplet. I hope that is okay. If you prefer another attribution other than "miplet," please let me know.

Using my table is fine with me. "miplet" is prefered. My sim was a quick million hands using php's shuffle function, so I don't realy know how random it is. (I have 2 c++ books sitting around that I should read.)

Ah, Mr. Bond; I've been expecting you....

:)

Thanks very much for the input, Wizard. Most helpful.

(BTW - you also need to edit the text that goes with the table, as "In the case of your example of 4 higher ranks and 9 total players, the probability is 16.89%" still refers to the old calculation. The value in the updated table is 16.45%.)

Cheers!
p

Quote: Wizard

If c is the number of overcards and p is the number of total players, including yourself, then the answer should been:

1-(1-(combin(8,2)-if(c<=6:combin(8-c,2),0)))/combin(45,2))^(n-1)

Hi Wiz!

Apologies if I seem to be turning into your NetNemesis, but that formula isn't right:-

* shouldn't it be combin(45,2))^(p-1), if p is the number of players? and
* you've got one too many/too few brackets

Cheers!
p-1 (hee hee! the leetle joke I am makings!)

Quote: miplet

Using my table is fine with me. "miplet" is prefered. My sim was a quick million hands using php's shuffle function, so I don't realy know how random it is. (I have 2 c++ books sitting around that I should read.)

I'm not sure how good it is either, but in general don't trust off the shelf RNG's very much. I highly recommend a compiled langauge for big simulations, and a Mersenne Twister for an RNG. Once you know one language picking up others is easy. It also looks great on a resume to list as many computer languages and skills as possible.

Anyway, thanks for the use of the table. If you ever redo it, let me know and I'll update the table.

Quote: podski

Hi Wiz!

* shouldn't it be combin(45,2))^(p-1), if p is the number of players?

Dang, I knew I should have double checked that. Thanks also for the correction on the example.

Quote: Wizard

Dang, I knew I should have double checked that. Thanks also for the correction on the example.

Really, don't mention it, Sir.

So...Wizard 'n' miplet - any thoughts on the other bit:

Quote: podski

is there a method generic enough to be applied across all other scenarios?

e.g. if i can calculate the heads-up (i.e. 1 opponent or 2 total players) probability of the other player having a better hand than me given my pocket cards and the Flop/Turn/River, can I then infer/simulate the probabilities for 2, 3....n other players?

Thanling You most politely,
p

Quote: podski

Thanling You most politely,

as in "Thanking You", obviously