Poll

4 votes (50%)
1 vote (12.5%)
3 votes (37.5%)

8 members have voted

gordonm888
gordonm888
Joined: Feb 18, 2015
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Thanks for this post from:
charliepatrick
April 26th, 2020 at 10:57:22 PM permalink
Quote: charliepatrick

A quick look (it's well past wine o'clock here!) I get a different answer, so I'm wondering whether I've got some wrong assumptions. For instance I am assuming that you only hold cards that could make a Royal Flush. So from AsAhAcAdKd you only hold AdKd.

From a probability point of view if you get multiple choices then pick one but the odds of then making a Royal are the same. i.e. you may have 2 of the 5, but still need the other 3, so it makes no difference whether you keep AK or QJ. However in practice you'd play QJ from AsKsQhJh7d as you have more outs.

Catch
1st Perms
2nd Perms
Contribution
5
4
1 533 939
6 135 756
4
940
163 185
153 393 900
3
43 240
14 190
613 575 600
2 2
25 200
946
23 839 200
2
597 000
946
564 762 000
1 1 1 1
20 000
43
860 000
1 1 1
248 000
43
10 664 000
1 1
744 000
43
31 992 000
1
719 200
43
30 925 600
0
201 376
4
805 504
2 598 960
0
1 436 953 560
2 774.374



Charlie, I am in perfect agreement with your 2nd column that is labeled "1st perms."

Its your third column and fourth columns that I don't agree with. Example: for all the initial hands in which you are drawing 4 cards to a Royal Flush, the probability of making the Royal on the draw is 1/combin(47,4). For the hands in which you are drawing 3 cards to a royal, the probability of the royal is 1/combin(47,3).

When summing cases with different numbers of cards being drawn, I found it was easier to convert to probabilities before summing.
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
charliepatrick
charliepatrick
Joined: Jun 17, 2011
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April 27th, 2020 at 1:46:28 AM permalink
Thanks - I can see it's easier to use probabilities for the second part. As an example my error was using perms saying you needed say 2 specific cards (1*1) then any 47 46 45 cards but assuming they could come in any order within five cards. I forgot to remember you were only drawing two cards. The last column is 4*1/combin(47,5) as you can catch any of the four suits.
Catch
Perms
1st Prob
2nd Prob
Contribution
5
4
.000 001 539
1.000 000 000
.000 001 539
4
940
.000 361 683
.021 276 596
.000 007 695
3
43 240
.016 637 424
.000 925 069
.000 015 391
2 2
25 200
.009 696 186
.000 061 671
.000 000 598
2
597 000
.229 707 268
.000 061 671
.000 014 166
1 1 1 1
20 000
.007 695 386
.000 005 606
.000 000 043
1 1 1
248 000
.095 422 784
.000 005 606
.000 000 535
1 1
744 000
.286 268 353
.000 005 606
.000 001 605
1
719 200
.276 726 075
.000 005 606
.000 001 551
0
201 376
.077 483 301
.000 002 608
.000 000 202
2 598 960
1.000 000 000
.000 043 326
23 080.747
DRich
DRich
Joined: Jul 6, 2012
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April 27th, 2020 at 3:54:47 PM permalink
On this Royal at all cost strategy would you hold the ten in this dealt scenarios 10h 9c 9s 9d 9h?
Living longer does not always infer +EV
michael99000
michael99000
Joined: Jul 10, 2010
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April 27th, 2020 at 4:02:14 PM permalink
What would be the Royal at All Costs play with this hand. ?

5h 10c Js Qd Kh
AxelWolf
AxelWolf
Joined: Oct 10, 2012
  • Threads: 146
  • Posts: 18246
April 27th, 2020 at 4:31:47 PM permalink
Quote: michael99000

What would be the Royal at All Costs play with this hand. ?

5h 10c Js Qd Kh

Are we assuming there's other pays and they actually matter? If not, would it really matter? The king. If there are other paybacks that matter, I assume that Jack would be the proper hold.
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
DRich
DRich
Joined: Jul 6, 2012
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April 27th, 2020 at 4:51:05 PM permalink
Quote: AxelWolf

Are we assuming there's other pays and they actually matter? If not, would it really matter? The king. If there are other paybacks that matter, I assume that Jack would be the proper hold.



I would assume the jack.
Living longer does not always infer +EV
rsactuary
rsactuary
Joined: Sep 6, 2014
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  • Posts: 1687
April 27th, 2020 at 8:15:05 PM permalink
I would think you'd have to assume the regular paytable is there, so that you get paid on some hands that you might be able to draw to. So the K would likely be the last pick because it is suited with the 5 and less likely to form a flush.

I would go with the J as well for more straight possibilities.
smoothgrh
smoothgrh
Joined: Oct 26, 2011
  • Threads: 65
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April 27th, 2020 at 8:39:55 PM permalink
Quote: DRich

On this Royal at all cost strategy would you hold the ten in this dealt scenarios 10h 9c 9s 9d 9h?



I would hold my nose and the 10.

Iíve thrown away several dealt trips.
smoothgrh
smoothgrh
Joined: Oct 26, 2011
  • Threads: 65
  • Posts: 629
April 27th, 2020 at 8:40:43 PM permalink
Quote: michael99000

What would be the Royal at All Costs play with this hand. ?

5h 10c Js Qd Kh



I have been keeping the J.
smoothgrh
smoothgrh
Joined: Oct 26, 2011
  • Threads: 65
  • Posts: 629
April 27th, 2020 at 8:51:56 PM permalink
Through 500 hands:
Playing 5x$0.10
Starting amount: $400
Current: $269.50
Lost $130.50
165 won/500 games 33% win
47.8% payback

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