methodman: insurance bet has house edge of over 7%---

[Cacarulo]

> Below are the CA values for a 75% pen 6D TC +10 Hi-Lo.
> The ace is included in the count for the
> calculations. All subsets are included. The main 2
> things that might effect the calculation are the
> effect that player strategy has on the effects of
> removals and the cut-card effect. The insurance bet
> is considered to be 1 unit (not 1/2) so cut in half to
> compare. The first number is the floored value and
> the next few are examples of values at exact counts:
> Insurance Evs
> Count EV Var DI Prob
> 10 0.1760 2.1451 0.0821 4.38E-04
> --- --- --- --- ---
> 10.0000 0.1652 2.1379 0.0773 5.79E-06
> 10.0084 0.1424 2.1221 0.0671 2.34E-16
> 10.0094 0.1536 2.1300 0.0721 7.31E-12
> 10.0107 0.1590 2.1337 0.0745 1.66E-09
> .
> Or for those too lazy to divide:
> Floored TC +10: 8.8%
> Exact TC +10.0: 8.26%
> It would be very interesting to know if the two
> effects I mentioned can really have a .5% effect on
> the EV. I believe it would take a very long sim to
> iron out the answer though.

Hi MGP,

Your numbers are correct. I've run a sim and here are the answers:

 

  TC           Freq                       Ev                                            Var 

  12   0.00009285378541   0.22382552438806   2.17372765902047 

  11   0.00021569851073   0.19994489208461   2.15996693221388 

  10   0.00043843295279   0.17589339199250   2.14495490664587 

   9   0.00089064098712   0.15202976011635   2.12891671215531 

   8   0.00176137967811   0.12816996401316   2.11174242433803 

   7   0.00331475866953   0.10410479717340   2.09326698837888 

   6   0.00603561367811   0.08059751066116   2.07410155193638 

   5   0.01112230539056   0.05685868751924   2.05362577717283 

   4   0.01962108213305   0.03322377447406   2.03211995528375 

   3   0.03457947527039   0.00982534537893   2.00972880796711 

   2   0.06090772761373  -0.01337009314451   1.98645114746479 

   1   0.11053921934335  -0.03658386300062   1.96207775796733 

   0   0.23538910084979  -0.06128543294911   1.93495866275913 

  -1   0.21184303602575  -0.08197355213833   1.91130678461150 

  -2   0.13534473424464  -0.10398889248050   1.88519741776018 

  -3   0.07331581470815  -0.12747580047477   1.85627411981855 

  -4   0.04230586232618  -0.15077741614771   1.82648875463211 

  -5   0.02304485025322  -0.17392425686844   1.79582609600432 

  -6   0.01347158427039  -0.19670683656317   1.76459958388614 

  -7   0.00730066685837  -0.21963177967743   1.73213010167830 

  -8   0.00411761172103  -0.24232771663626   1.69894956111359 

  -9   0.00210944829185  -0.26503796371287   1.66471691407806 

 -10   0.00111180841631  -0.28721540667760   1.63029190348943 

 -11   0.00055178409871  -0.30942373080160   1.59483322401523 

 -12   0.00027849173391  -0.33168633047784   1.55829784769630 

 

Overall: 

 

Rounds = 233000000000 

 

Ev    = -0.073952 

Var   =  1.926048 

Sd    =  1.387821 

Se    =  0.000003 

Index =  +3 

Since we bet half a unit we should divide the expectations by 2.

Hope this helps.

Sincerely,
Cac

[MGP]

Thanks Cacarulo

I was hoping you might see this thread

 

> Hi MGP,  

> Your numbers are correct. I've run a sim and here are  

> the answers:  

>   TC       Freq                 EV                Var  

>   12   0.00009285378541   0.22382552438806   0.17372765902047  

>   11   0.00021569851073   0.19994489208461   2.15996693221388  

>   10   0.00043843295279   0.17589339199250   2.14495490664587  

>    9   0.00089064098712   0.15202976011635   2.12891671215531  

>    8   0.00176137967811   0.12816996401316   2.11174242433803  

>    7   0.00331475866953   0.10410479717340   2.09326698837888  

>    6   0.00603561367811   0.08059751066116   2.07410155193638  

>    5   0.01112230539056   0.05685868751924   2.05362577717283  

>    4   0.01962108213305   0.03322377447406   2.03211995528375  

>    3   0.03457947527039   0.00982534537893   2.00972880796711  

>    2   0.06090772761373  -0.01337009314451   1.98645114746479  

>    1   0.11053921934335  -0.03658386300062   1.96207775796733  

>    0   0.23538910084979  -0.06128543294911   1.93495866275913  

>   -1   0.21184303602575  -0.08197355213833   1.91130678461150  

>   -2   0.13534473424464  -0.10398889248050   1.88519741776018  

>   -3   0.07331581470815  -0.12747580047477   1.85627411981855  

>   -4   0.04230586232618  -0.15077741614771   1.82648875463211  

>   -5   0.02304485025322  -0.17392425686844   1.79582609600432  

>   -6   0.01347158427039  -0.19670683656317   1.76459958388614  

>   -7   0.00730066685837  -0.21963177967743   1.73213010167830  

>   -8   0.00411761172103  -0.24232771663626   1.69894956111359  

>   -9   0.00210944829185  -0.26503796371287   1.66471691407806  

>  -10   0.00111180841631  -0.28721540667760   1.63029190348943  

>  -11   0.00055178409871  -0.30942373080160   1.59483322401523  

>  -12   0.00027849173391  -0.33168633047784   1.55829784769630  

 

> Overall:  

> Rounds = 233000000000  

> Ev    = -0.073952  

> Var   =  1.926048  

> Sd    =  1.387821  

> Se    =  0.000003  

> Index =  +3  

>  

> Since we bet half a unit we should divide the  

> expectations by 2.  

> Hope this helps.  

> Sincerely,  

> Cac