Romes
Romes 
Joined: Jul 22, 2014
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July 18th, 2017 at 11:37:11 AM permalink
Quote: KevinAA

I have some statistics about the probability distribution of winning a royal flush given that you held 0,1,2,3,4 or all 5 cards to a royal flush from your dealt hand.

... go on...
Playing it correctly means you've already won.
PokerGrinder
PokerGrinder
Joined: Apr 30, 2015
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Romes
July 18th, 2017 at 11:46:17 AM permalink
Quote: Romes

... go on...


Lmao is this a na na na na na, I have the stats and you don't kind of thing?
You can shear a sheep a hundred times, but you can skin it only once. Amarillo Slim Preston
Wizardofnothing
Wizardofnothing
Joined: Jul 3, 2015
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Romes
July 18th, 2017 at 11:46:28 AM permalink
I don't get that post at all
NOW HIRING!!!! REQUEST INFO VIA PM
Ibeatyouraces
Ibeatyouraces
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July 18th, 2017 at 11:59:30 AM permalink
Quote: KevinAA

I have some statistics about the probability distribution of winning a royal flush given that you held 0,1,2,3,4 or all 5 cards to a royal flush from your dealt hand.



Well it depends. Are the card preshuffled in a Chinese prison?
"And that's the bottom lineeeee, cuz Stone Cold said so!"
KevinAA
KevinAA
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July 18th, 2017 at 12:21:23 PM permalink
Quote: Romes

... go on...



People were mean to me in my slot machine thread so I am sitting on the results. But I am a forgiving person... let me finish my cup of coffee and then I will release them. Attacks like those in my slot machine thread will result in the figures not being released.
monet0412
monet0412
Joined: Feb 18, 2016
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MaxPen
July 18th, 2017 at 12:33:23 PM permalink
Quote: KevinAA

People were mean to me in my slot machine thread so I am sitting on the results. But I am a forgiving person... let me finish my cup of coffee and then I will release them. Attacks like those in my slot machine thread will result in the figures not being released.



LOL

N=X if you do 1 Lap inside the Casino and cash out 3 times divided by the amount of spins on said machine equals 102.4% payback with no variance. If X=P you head directly to the restroom where P is always +EV!!
Romes
Romes 
Joined: Jul 22, 2014
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July 18th, 2017 at 12:33:45 PM permalink
Quote: KevinAA

People were mean to me in my slot machine thread so I am sitting on the results. But I am a forgiving person... let me finish my cup of coffee and then I will release them. Attacks like those in my slot machine thread will result in the figures not being released.

...and there are those of us whom had nothing to do with that and have no idea what you're even talking about (like me).

A helpful tip - Let haters hate and just try to do what you think is right... but trying to show "I'm holding information, ask nicely!" is no way to go about it. I just enjoy reading (correct) statistical information on just about anything I can, but I in no way, shape, or form need your figures. Would it be nice to read them? Sure. Do I really want to or need to? Nope. Enjoy your coffee =).
Playing it correctly means you've already won.
KevinAA
KevinAA
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July 18th, 2017 at 12:43:12 PM permalink
Quote: monet0412

LOL

N=X if you do 1 Lap inside the Casino and cash out 3 times divided by the amount of spins on said machine equals 102.4% payback with no variance. If X=P you head directly to the restroom where P is always +EV!!



I never said any such thing. Stop putting words in my mouth.
monet0412
monet0412
Joined: Feb 18, 2016
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July 18th, 2017 at 1:04:18 PM permalink
Quote: KevinAA

Quote: monet0412

LOL

N=X if you do 1 Lap inside the Casino and cash out 3 times divided by the amount of spins on said machine equals 102.4% payback with no variance. If X=P you head directly to the restroom where P is always +EV!!



I never said any such thing. Stop putting words in my mouth.



What did that guy in that Batman movie say... Why soooooo serious???
KevinAA
KevinAA
Joined: Jul 6, 2017
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July 18th, 2017 at 1:12:23 PM permalink
Quote: Romes

...and there are those of us whom had nothing to do with that and have no idea what you're even talking about (like me).

A helpful tip - Let haters hate and just try to do what you think is right... but trying to show "I'm holding information, ask nicely!" is no way to go about it. I just enjoy reading (correct) statistical information on just about anything I can, but I in no way, shape, or form need your figures. Would it be nice to read them? Sure. Do I really want to or need to? Nope. Enjoy your coffee =).



single drawing double double bonus with a paytable 1-1-3-4-6-9-50-80-160-160-400-50-800

I wrote a program to go through all 2,598,960 (52 choose 5) possible initial hands. For each hand, the program selects which cards to hold using basic strategy. The program then outputs one row indicating whether a royal flush is possible (e.g., not possible if you hold a pair), and if possible, how many royal flush cards were held (0, 1, 2, 3, 4 or all 5). I didn't need the program to go through all possible drawn cards for the n to a royal flush hands because the probability of winning a royal flush given you hold n to a royal flush can be calculated exactly.

If you get a garbage hand with a 10 in it (2 3 7 8 10 different suits), the probability of winning a royal flush is 3 in 47 choose 5.
If you get a garbage hand without a 10 in it (2 3 7 8 9 different suits), the probability of winning a royal flush is 4 in 47 choose 5. If you hold a single J, Q, K or A (with no 10 same suit), the probability of winning a royal flush is 1 in 47 choose 4. Etc... holding 4 to a royal flush has a 1 in 47 chance of winning a RF, and of course being dealt a royal flush has a 100% chance of winning a RF.

Of the 2.6 million possible initial hands, 64% of them cannot result in a royal flush (hold a pair, or 4 to a flush, etc.). For the rest, I took the number of hands and multiplied by the probability of winning a royal flush to get the expected value for number of RF. I then took each n=0,1,2,3,4,5 to a royal flush expected values of winning a RF divided by the total to get the share of all RF's that started with n=0,1,2,3,4,5 to a royal flush.

n to a RF  hands   prob(win RF)  1 in    exp val     share of RF
0 no 10 58884 2.60767E-06 383,485 0.153549783 both zeroes below
0 w/10 52080 1.95575E-06 511,313 0.101855419 0.40%
1 585672 5.60648E-06 178,365 3.283558994 5.20%
2 201240 6.16713E-05 16,215 12.4107308 19.65%
3 25188 0.000925069 1,081 23.30064755 36.89%
4 936 0.021276596 47 19.91489362 31.53%
5 4 1 1 4 6.33%
total 63.16523617 100.00%


What this means is that of all royal flush winners, the most common ones held 3 to a royal flush -- 37% of them. That is followed by those who held 4 to a royal flush, 31.5%. Then 2 suited face cards, 20%, then a big drop to being dealt a royal flush, 6.33% of all royal flush winners, then just 1 face card at 5.2%, and the smallest share is garbage hand, only 0.4%.

The probability of being dealt a garbage hand and then winning a royal flush is 58884/2598960*2.60767E-06+52080/2598960*1.95575E-06 which is 9.82721E-08, or 1 in 10,175,830! No extra prize for that, but that's a royal flush win to be extra excited about, right? :)

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