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A simple blackjack variant


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20 replies to this topic

#11 TheChad08

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Posted 26 October 2012 - 02:38 AM

Oops, forgot to put my post in spoilers.

Sorry about that.

As for the calculations, I don't know how to write programs to do that for me as there would be thousands of possibilities.
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#12 superprismatic

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Posted 26 October 2012 - 05:14 PM

Spoiler for I wrote a simulator and

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#13 CaptainEd

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Posted 26 October 2012 - 06:14 PM

Would you say the winning seat benefited more from 20/21 or from the other two going bust?
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#14 superprismatic

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Posted 26 October 2012 - 06:28 PM

Would you say the winning seat benefited more from 20/21 or from the other two going bust?

I don't know, but I can modify my program to count those things. I have an appointment soon.
When I return from that, I'll fix up the program. Perhaps knowing such things may make it easier
to analyse the problem analytically.
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#15 Yoruichi-san

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Posted 26 October 2012 - 08:54 PM

Spoiler for A good starting point

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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page!  Episode 3 is finally here!

When life hands me lemons, I make invisible ink.


#16 superprismatic

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Posted 26 October 2012 - 09:45 PM

Would you say the winning seat benefited more from 20/21 or from the other two going bust?

Spoiler for I did another simulation for the Captain

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#17 CaptainEd

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Posted 26 October 2012 - 10:41 PM

Thank you, Superprismatic! (And thank you, Y-san. Such a simple question, with so little intuition available for guessing how it should go, and such a tiny, but repeatable effect. Great fun!)

I'm quite surprised how much more important the ability to hit 20/21 is than the ability to be the survivor. Over 80% of the wins due to 20/21!

And yet, even so, the first position is only very slightly stronger than the other two...
Fascinating!
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#18 brifri238

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Posted 02 November 2012 - 04:16 PM

Similar to Superprismatic I too ran a simulation (over only a mere 100,000,000 hands) and got similar results with Hand1 winning and Hand 3 in second.(Hand1: 34.257% / Hand3: 33.854% / Hand2: 31.889%). I also ran the simulation for a 'REAL WORLD' execution using one deck of cards without replacement. (Other assumptions the same, and in addition: if a hand goes over 21 no further cards are dealt to that person during that round-[this assumption is irrelevant when using an infinite number of decks]). In this case Hand 3 is the most likely to win! - (Hand 3: 34.0045 %, Hand 1 in a close second with 33.9777 % and Hand 2 with 32.0178%)

Edited by brifri238, 02 November 2012 - 04:18 PM.

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#19 brifri238

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Posted 05 November 2012 - 09:47 AM

I re-ran both my simulations: scenario 1: with an infinite number of card decks, and the more real world scenario 2: with one deck of cards where cards are dealt without replacement. Both simulations were run over 1000,000,000 hands and the previous results and rankings were confirmed:

Scenario 1: (infinite number of decks): Hand 1 (34.2521%), Hand3 (33.8808%) and Hand 2 (31.8671%)

Scenario 2: (one deck without replacement): Hand 3 (34.0031%), Hand 1(33.9674%) and Hand 2 (32.0294%)

Edited by brifri238, 05 November 2012 - 09:50 AM.

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#20 Yoruichi-san

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Posted 05 November 2012 - 07:35 PM

Wow, that's pretty interesting, thanks brifri ^_^ .

If anyone is still attempting the semi-analytical approach, I find that comparing the winning chances of each chair during a round is a good way to do it.
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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page!  Episode 3 is finally here!

When life hands me lemons, I make invisible ink.





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