Useless info or guide to efficiency?

[New2vp]

Webman's recent posting of a fun fact caused me to think of another.  What percentage of dealt cards are kept when making the proper strategic choice?  Of course the answer depends on the game.With 9/6 Jacks or Better, the answer is 41.6701% (if you hold 4 when dealt quads; a slightly higher percentage if you hold 5).  You hold 5,414,952 of the 5 x 2,598,960 = 12,994,880 cards that can be dealt, summing over all the possible combinations.With Full Pay Deuces Wild, you have nearly 2 1/2 times as many hands where you hold all 5, but almost 5 times as many hands when you toss all of them.  Overall, you hold 38.5997% of the cards that are dealt, 7.36% fewer held cards than 9/6 Jacks or Better [(41.6701 - 38.5997)/41.6701].



9/6 Jacks or Better


Holding 5
when dealt quads


    Starting Hands
      Cards Held


19488
5


292176
4


147528
3


1651440
2


403968
1


84360
0






2598960
5415576


12994800
41.6749%






9/6 Jacks
or Better


Holding 4
when dealt quads


    Starting Hands
      Cards Held


18864
5


292800
4


147528
3


1651440
2


403968
1


84360
0






2598960
5414952


12994800
41.6701%






Full Pay
Deuces Wild


    Starting Hands
      Cards Held


64380
5


264724
4


449816
3


961200
2


363312
1


495528
0






2598960
5015956


12994800
38.5997%

Bob Dancer in the Special Feature video in VPFW says that Deuces Wild is, in his opinion, the most fun game; and that, if he has a choice to play 2 games that are otherwise equal in value, he will select Deuces Wild every time.After thinking about this, I wonder if he is making this choice for efficiency:  to save himself 7% of the work necessary in pushing the hold buttons.Edit:  When compiling these numbers, I did not consider that the 4 dealt royal flush hands would be autoheld, but I suppose that could modify the hold percentages slighlty!

[jm002546]

FPDW has a very easy strategy and can be played faster than other games, for most people.  But it seems to be disappearing so I am switching to double bonus.  

[shadowman]

Both JOB and FPDW are somewhat boring. The problem in deuces is all the throw away hands. Both games are much better in multi-play but those are hard, if not impossible, to find.

 
I think some people find the easy strategies for these games to be a plus. For me, that adds to the boredom. Good thing we're all different or we'd all end up playing the same machine.

[shadowman]

Nice analysis, new. I would have guessed a little higher. Now, if asked, I can just say the average is about 2 cards knowing that is real close.