100xOdds
100xOdds
Joined: Feb 5, 2012
  • Threads: 516
  • Posts: 3054
November 27th, 2019 at 6:41:47 AM permalink
Variance in Blackjack = ~4.
in video poker, variance of Jacks or Better = ~19.
For Ultimate Texas Holdem table game, the Wiz has said the variance is ~25.

What's the variance for passline (or dont pass) for:
1) 2x odds
2) 3/4/5x odds?

thx
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
odiousgambit
odiousgambit
Joined: Nov 9, 2009
  • Threads: 306
  • Posts: 8407
November 27th, 2019 at 6:57:11 AM permalink
The variance for BJ is about 1, not 4, btw. It's the main reason I won't play BJ much

For Craps, the below was posted by Alan Shank [goatcabin]. I saved it but failed to save the url for the post

note he lists the SD
_

Odds unitSD avg bet
0 0.999900005 1.00
1 1.893050027 1.67
2 2.857879771 2.33
Full 2 2.954695498 2.47
3 3.840744091 3.00
345X 4.91563184 3.78
4 4.830647323 3.67
5 5.824001368 4.33
6 6.819298375 5.00
7 7.815796102 5.67
8 8.813087262 6.33
9 9.810929899 7.00
10 10.80917128 7.67
20 20.80087901 14.33
40 40.7964868 27.67
50 50.7955876 34.33
60 60.79498419 41.00
80 80.79422548 54.33
100 100.7937679 67.6
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
7craps
7craps
Joined: Jan 23, 2010
  • Threads: 18
  • Posts: 1977
Thanks for this post from:
ChumpChange
November 27th, 2019 at 7:41:28 AM permalink
mine is similar
craps pass line
OddsVarunit SDavg bet
00.999800020.9999000051
13.5836384041.8930500271.666666667
28.1674767882.8578797712.333333333
Full 2x8.7302254872.9546954982.47
314.751315173.8407440913
345X24.163436384.915631843.78
423.335153564.8306473233.666666667
533.918991945.8240013684.333333333
646.502830326.8192983755
761.086668717.8157961025.666666667
877.670507098.8130872626.333333333
996.254345479.8109298997
10116.838183910.809171287.666666667
20432.676567720.8008790114.33333333
401664.35333540.796486827.66666667
502580.19171950.795587634.33333333
603696.03010360.7949841941
806527.70687180.7942254854.33333333
10010159.38364100.793767967.66666667
winsome johnny (not Win some johnny)
100xOdds
100xOdds
Joined: Feb 5, 2012
  • Threads: 516
  • Posts: 3054
November 27th, 2019 at 7:53:24 AM permalink
Quote: odiousgambit

The variance for BJ is about 1, not 4, btw. It's the main reason I won't play BJ much

For Craps, the below was posted by Alan Shank [goatcabin]. I saved it but failed to save the url for the post

note he lists the SD
_

Odds unitSD avg bet
0 0.999900005 1.00
1 1.893050027 1.67
2 2.857879771 2.33
Full 2 2.954695498 2.47
3 3.840744091 3.00
345X 4.91563184 3.78
4 4.830647323 3.67
5 5.824001368 4.33
6 6.819298375 5.00
7 7.815796102 5.67
8 8.813087262 6.33
9 9.810929899 7.00
10 10.80917128 7.67
20 20.80087901 14.33
40 40.7964868 27.67
50 50.7955876 34.33
60 60.79498419 41.00
80 80.79422548 54.33
100 100.7937679 67.6

thx!
interesting.. the higher the odds, the lower the house edge but the higher the variance.

as for my questions, i see from your chart:
2x odds = 8 var
3/4/5x = 24 var

so basically not much difference between 3/4/5x craps and ultimate texas holdem in terms of both house edge* and variance.
*.6% if you follow the Wiz's strat for uth vs .4% for 3/4/5x odds.

why wont you play blackjack because of low var?
why is var = 1 bad?
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
ChesterDog
ChesterDog 
Joined: Jul 26, 2010
  • Threads: 7
  • Posts: 922
November 27th, 2019 at 8:36:18 AM permalink
Quote: 100xOdds

Variance in Blackjack = ~4.
in video poker, variance of Jacks or Better = ~19.
For Ultimate Texas Holdem table game, the Wiz has said the variance is ~25.

What's the variance for passline (or dont pass) for:
1) 2x odds
2) 3/4/5x odds?

thx



I found the variance for the don't pass (counting 12 as push,) and here are my results:
Bet
Odds
Variance
S.D.
pass
2
8.16747679
2.85787977
pass
345
24.16343638
4.91563184
don't pass
2
8.13971304
2.85301823
don't pass
345
24.13567264
4.91280700


Also, here's the Wizard's page on variance in blackjack: https://wizardofodds.com/games/blackjack/variance/.
odiousgambit
odiousgambit
Joined: Nov 9, 2009
  • Threads: 306
  • Posts: 8407
November 27th, 2019 at 10:40:15 AM permalink
Quote: 100xOdds

why wont you play blackjack because of low var?
why is var = 1 bad?

of course low variance means your sessions tend to stick more to the expected value, which is negative

Mathematically you can look at EV/SD ... in BJ your EV will approach the value of the SD rapidly. When it reaches 1 SD you can truly call yourself a fool for playing so long ... you had to have been lucky by a factor of 1 SD just to break even.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
DogHand
DogHand
Joined: Sep 24, 2011
  • Threads: 1
  • Posts: 403
November 27th, 2019 at 12:33:43 PM permalink
Quote: ChesterDog

<snip>Also, here's the Wizard's page on variance in blackjack: https://wizardofodds.com/games/blackjack/variance/.



ChesterDog,

Thanks for the link: the photograph alone made it worth clicking, but left me wondering why the dealer drew a 7? And where are $25 chips purple?

Dog Hand
ChesterDog
ChesterDog 
Joined: Jul 26, 2010
  • Threads: 7
  • Posts: 922
Thanks for this post from:
odiousgambit
November 27th, 2019 at 12:56:37 PM permalink
Quote: DogHand

Quote: ChesterDog

<snip>Also, here's the Wizard's page on variance in blackjack: https://wizardofodds.com/games/blackjack/variance/.



ChesterDog,

Thanks for the link: the photograph alone made it worth clicking, but left me wondering why the dealer drew a 7? And where are $25 chips purple?

Dog Hand



That's a good question!

I can only guess that the dealer was probably male and completely distracted.
100xOdds
100xOdds
Joined: Feb 5, 2012
  • Threads: 516
  • Posts: 3054
November 27th, 2019 at 3:51:42 PM permalink
Quote: odiousgambit

of course low variance means your sessions tend to stick more to the expected value, which is negative

Mathematically you can look at EV/SD ... in BJ your EV will approach the value of the SD rapidly. When it reaches 1 SD you can truly call yourself a fool for playing so long ... you had to have been lucky by a factor of 1 SD just to break even.

ahh...
9/7 triple double bonus in vp has a var = ~90.
payback is 99.6%.
but you'll be losing BIG time until you hit one of the 3 big hands (Royal, quad aces with kicker, quad babies with kicker).

so i guess the higher the var, the longer the comitment (ie: deep pockets) to play the game till the variance evens out?
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)

  • Jump to: