100xOdds
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May 26th, 2017 at 4:43:00 PM permalink
Lets say you have 2 games close in Return but a huge difference in Variance.

Variance of $2 9/6 Jacks or Better (99.54%): 19.51
Variance of $2 9/7 Triple double bonus (99.58%) : 98.28

If $50k coin-in (for DiaD):
Expected loss 9/6 JoB = -$230 +/- $3123
Expected loss 9/7 tdb = -$210 +/- $7010

And that's just 1 standard deviation (for 68% chance your play falls in that range).
if 2 SD (for 95% of all possible results), double it.

ie: 9/7 tdb = -$210 +/- $14k for 2 sd

Most people would sacrifice the .04% return and pick 9/6 JoB over 9/7 tdb.
But at what point is it worth picking the higher variance game?

For example:
Multistrike (9/6 JoB) is 99.79% with Variance = 308

Is .25% better return but 16x the variance of regular JoB worth it?

Is there a sweet spot or a rule of thumb for Return vs Variance when deciding on which game to play?
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billryan
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May 26th, 2017 at 4:55:58 PM permalink
I'll let someone else do the math and approach this from a different angle. Playing TDB, you will lose more often and lose more per visit.
Most casinos seem to reward cashback in mailings at least partially for what you lose, so a person who has four sessions in a month of -1000,-1000,-1000, + 2700 will get much more cashback than someone who does -150, +200, -200,-150 even though in the end they each lost $300 for the month, and had the same coin in.
Bigger losses seems to equal bigger mailings.
I know that doesn't answer your question but helps explain why a higher variance game is better, IF you are properly funded.
Last edited by: billryan on May 26, 2017
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Ibeatyouraces
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May 26th, 2017 at 8:42:49 PM permalink
Personally I'd do the JoB because I can get it done much faster as the strategy is easy and I wouldn't spend time thinking about (or looking up) the proper play. That and the variance certainly.
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RS
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May 26th, 2017 at 10:54:41 PM permalink
Quote: 100xOdds

Lets say you have 2 games close in Return but a huge difference in Variance.

Variance of $2 9/6 Jacks or Better (99.54%): 19.51
Variance of $2 9/7 Triple double bonus (99.58%) : 98.28

If $50k coin-in (for DiaD):
Expected loss 9/6 JoB = -$230 +/- $3123
Expected loss 9/7 tdb = -$210 +/- $7010

And that's just 1 standard deviation (for 68% chance your play falls in that range).
if 2 SD (for 95% of all possible results), double it.

ie: 9/7 tdb = -$210 +/- $14k for 2 sd

Most people would sacrifice the .04% return and pick 9/6 JoB over 9/7 tdb.
But at what point is it worth picking the higher variance game?

For example:
Multistrike (9/6 JoB) is 99.79% with Variance = 308

Is .25% better return but 16x the variance of regular JoB worth it?

Is there a sweet spot or a rule of thumb for Return vs Variance when deciding on which game to play?


There isn't really a "rule of thumb" for this. Maybe for each individual there is, to roughly estimate it for yourself, but not in general. With many things in gambling and much in life in general -- it depends.

If someone has a $20k bankroll and someone else has $2M bankroll, they might have very different answers for the same play.

I'd rather play something around $10-25 a spin and get the play over with in 1-3 hours, while someone else (say, MaxPen for example) would rather play $0.05 single line for 22 hours straight (inside joke!)....and the decision has nothing to do with bankroll. If giving up 0.2% means I'm done in 1 hour instead of 5.....looks like I'm gonna be giving up 0.2% for the play. If giving up 0.2% means I'll cut my variance in half, then I'll be giving up 0.2% on the play. Sometimes I'll give up more and sometimes I wouldn't be able to afford to give up that amount.


One way to determine which is better is to calculate the CE: Certainty Equivalent. That's actually probably the easiest and best way to get a good answer on this. Anything else is speculation and making an educated guess.
100xOdds
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May 27th, 2017 at 1:20:36 AM permalink
Quote: RS

One way to determine which is better is to calculate the CE: Certainty Equivalent. That's actually probably the easiest and best way to get a good answer on this. Anything else is speculation and making an educated guess.


whats the Formula?
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RS
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May 27th, 2017 at 2:02:18 AM permalink
Quote: 100xOdds

Quote: RS

One way to determine which is better is to calculate the CE: Certainty Equivalent. That's actually probably the easiest and best way to get a good answer on this. Anything else is speculation and making an educated guess.


whats the Formula?


https://www.blackjackapprenticeship.com/math-behind-advantage-play/

EV-( (bet size*Standard Deviation)^2)/(2*Kelly factory*BR)
odiousgambit
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May 27th, 2017 at 3:58:56 AM permalink
Quote: 100xOdds

Variance of $2 9/6 Jacks or Better (99.54%): 19.51
Variance of $2 9/7 Triple double bonus (99.58%) : 98.28

I might want better variance at times than JoB gives but I would dislike playing a game with variance of 98 'just about no matter what. '
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
100xOdds
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May 27th, 2017 at 6:10:25 AM permalink
Quote: RS

https://www.blackjackapprenticeship.com/math-behind-advantage-play/

EV-( (bet size*Standard Deviation)^2)/(2*Kelly factory*BR)


thx.
I read in bj, if Kelly = 1/2 = 50% = .5 then you have 0.1% probability of losing 90% of bankroll.

what to use in VP?
same?

For example, using BankRoll = 125% of 1 sd for each game:
CE ($2 9/6 JoB for 5k hands <$50k coin-in>)= -$230 - (($10*4.42)^2)/(2*.5*$4000) = -$230.49
CE ($2 9/7 tdb for 5k hands <$50k coin-in>) = -$210 - (($10*9.91)^2)/(2*.5*$9000) = -$211.09
CE ($0.50 Multistrike (9/6 JoB) for 5k hands <$50k coin-in>) = -$105 - ($10*17.55)^2/(2*.5*$15500) = -$106.99

if my math is right, Multistrike even with it's HUGE variance is the better game to play since I lose the least?

hm.. lets see what happens if I used a fixed bankroll (ie: $4k) for all.
ce (JoB) = -$230.49
ce (tdb) = -212.46
ce (multistrike) = -112.7

Multistrike still wins?
so Return is king and variance means little?!

Or am I doing something wrong?
If so, WHAT?
Last edited by: 100xOdds on May 27, 2017
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
100xOdds
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May 27th, 2017 at 6:50:16 AM permalink
Quote: odiousgambit

I might want better variance at times than JoB gives but I would dislike playing a game with variance of 98 'just about no matter what. '


I never knew the variance of Multistrike was sooooooooooooo high (even JoB variety) till I created this thread.

no wonder I lost $1400 quick at $0.50 denom as if I was in a full nude strip bar that served free alcohol.
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FleaStiff
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May 27th, 2017 at 7:19:48 AM permalink
Quote: billryan

casinos reward in mailings for what you lose, so Bigger losses equal bigger mailings.

True, but mailings are frosting on the cake. A mailing is good, a really generous mailing is better, if MY mailing is better than YOURS I may feel that "I've won" against you. If my mailing is better than it otherwise would be, I may feel like "I've won" against the casino's computerized mailing program. Perhaps I have won against the casino's mailing program, but any way you look at it what really counts is what takes place in the casino.

So it takes a fully funded 'staying power' to be able to outlast that variance factor and receive the enhanced mailing.
Ibeatyouraces
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May 27th, 2017 at 7:37:57 AM permalink
You can't guarantee mailers either.
DUHHIIIIIIIII HEARD THAT!
RS
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May 27th, 2017 at 9:43:45 AM permalink
Quote: 100xOdds

thx.
I read in bj, if Kelly = 1/2 = 50% = .5 then you have 0.1% probability of losing 90% of bankroll.

what to use in VP?
same?

For example, using BankRoll = 125% of 1 sd for each game:
CE ($2 9/6 JoB for 5k hands <$50k coin-in>)= -$230 - (($10*4.42)^2)/(2*.5*$4000) = -$230.49
CE ($2 9/7 tdb for 5k hands <$50k coin-in>) = -$210 - (($10*9.91)^2)/(2*.5*$9000) = -$211.09
CE ($0.50 Multistrike (9/6 JoB) for 5k hands <$50k coin-in>) = -$105 - ($10*17.55)^2/(2*.5*$15500) = -$106.99

if my math is right, Multistrike even with it's HUGE variance is the better game to play since I lose the least?

hm.. lets see what happens if I used a fixed bankroll (ie: $4k) for all.
ce (JoB) = -$230.49
ce (tdb) = -212.46
ce (multistrike) = -112.7

Multistrike still wins?
so Return is king and variance means little?!

Or am I doing something wrong?
If so, WHAT?


Why do you set bankroll to 125% of 1 SD? Your bankroll is your bankroll. Doesn't matter what the SD is of a game.

Also, EV is per hand, not overall.
AxelWolf
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May 27th, 2017 at 9:51:28 AM permalink
Quote: RS

Quote: 100xOdds

thx.
I read in bj, if Kelly = 1/2 = 50% = .5 then you have 0.1% probability of losing 90% of bankroll.

what to use in VP?
same?

For example, using BankRoll = 125% of 1 sd for each game:
CE ($2 9/6 JoB for 5k hands <$50k coin-in>)= -$230 - (($10*4.42)^2)/(2*.5*$4000) = -$230.49
CE ($2 9/7 tdb for 5k hands <$50k coin-in>) = -$210 - (($10*9.91)^2)/(2*.5*$9000) = -$211.09
CE ($0.50 Multistrike (9/6 JoB) for 5k hands <$50k coin-in>) = -$105 - ($10*17.55)^2/(2*.5*$15500) = -$106.99

if my math is right, Multistrike even with it's HUGE variance is the better game to play since I lose the least?

hm.. lets see what happens if I used a fixed bankroll (ie: $4k) for all.
ce (JoB) = -$230.49
ce (tdb) = -212.46
ce (multistrike) = -112.7

Multistrike still wins?
so Return is king and variance means little?!

Or am I doing something wrong?
If so, WHAT?


Why do you set bankroll to 125% of 1 SD? Your bankroll is your bankroll. Doesn't matter what the SD is of a game.

Also, EV is per hand, not overall.

If you are a true AP your Bankroll includes the lint in your pocket. Hopefully you can turn that lint into gold if need be.
♪♪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♪♪
billryan
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May 27th, 2017 at 10:28:48 AM permalink
Quote: FleaStiff

True, but mailings are frosting on the cake. A mailing is good, a really generous mailing is better, if MY mailing is better than YOURS I may feel that "I've won" against you. If my mailing is better than it otherwise would be, I may feel like "I've won" against the casino's computerized mailing program. Perhaps I have won against the casino's mailing program, but any way you look at it what really counts is what takes place in the casino.

So it takes a fully funded 'staying power' to be able to outlast that variance factor and receive the enhanced mailing.



I disagree. Winnings from the casino are just one leg of a three legged stool.
Cash back and comps are just as important and valuable. Few people will be overall winners unless they max out all three. Who wants a cake with no frosting? I want mine to be Devils Food, with Vanilla Icing with money baked in.
The difference between fiction and reality is that fiction is supposed to make sense.
billryan
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May 27th, 2017 at 10:29:59 AM permalink
Quote: Ibeatyouraces

You can't guarantee mailers either.



What can you guarantee?
The difference between fiction and reality is that fiction is supposed to make sense.
Ibeatyouraces
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May 27th, 2017 at 10:35:12 AM permalink
Quote: billryan

What can you guarantee?


Just death.
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100xOdds
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May 27th, 2017 at 2:32:29 PM permalink
Quote: RS

Why do you set bankroll to 125% of 1 SD? Your bankroll is your bankroll. Doesn't matter what the SD is of a game.

Also, EV is per hand, not overall.


ok, so $4k bankroll for all.
ahh.. EV per hand.

will do new calcs after dinner :)
Last edited by: 100xOdds on May 27, 2017
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rsactuary
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May 27th, 2017 at 3:45:48 PM permalink
Quote: Ibeatyouraces

Just death.



and taxes
Ibeatyouraces
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May 27th, 2017 at 3:49:28 PM permalink
Quote: rsactuary

and taxes


You can't guarantee that. Plenty of people that never pay taxes.
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RS
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May 27th, 2017 at 3:52:00 PM permalink
Quote: Ibeatyouraces

You can't guarantee that. Plenty of people that never pay taxes.


Property tax, sales tax, tobacco tax, gas tax, etc. ?
Ibeatyouraces
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May 27th, 2017 at 3:55:06 PM permalink
Quote: RS

Property tax, sales tax, tobacco tax, gas tax, etc. ?


Just be homeless and beg.

Humans can eliminate taxes of they wanted to. You can't eliminate death.
DUHHIIIIIIIII HEARD THAT!
100xOdds
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May 27th, 2017 at 4:05:58 PM permalink
Quote: RS

Also, EV is per hand, not overall.


New calcs (and using a $4k bankroll for all):
CE ($2 9/6 JoB)= -$0.46 - (($10*4.42)^2)/(2*.5*$4000) = -$.95
CE ($2 9/7 tdb) = -$.42 - (($10*9.91)^2)/(2*.5*$4000) = -$2.88
CE ($0.50 Multistrike (9/6 JoB)) = -$.21 - ($10*17.55)^2/(2*.5*$4000) = -$7.91

so lower variance is king and trumps return.
Thus plain old 9/6 JoB is the winner.

interesting enough, even with $100k bankroll, 9/6 JoB is still the winner but Multistrike came in 2nd by a hair.
so with enough bankroll, return will overcome variance.

edit:
does Kelly Factor even matter since it's the same for all 3 games?
Last edited by: 100xOdds on May 27, 2017
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Ibeatyouraces
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May 27th, 2017 at 4:09:29 PM permalink
Quote: 100xOdds

New calcs (and using a $4k bankroll for all):
CE ($2 9/6 JoB)= -$0.46 - (($10*4.42)^2)/(2*.5*$4000) = -$.95
CE ($2 9/7 tdb) = -$.42 - (($10*9.91)^2)/(2*.5*$4000) = -$2.88
CE ($0.50 Multistrike (9/6 JoB)) = -$.21 - ($10*17.55)^2/(2*.5*$4000) = -$7.91

so lower variance is king and trumps return.
Thus 9/6 JoB is the winner.

interesting enough, even with $100k bankroll, 9/6 JoB is still the winner but Multistrike came in 2nd by a hair.


I'm gonna jinx you now and say you'll get AWAK at least twice. :-)
DUHHIIIIIIIII HEARD THAT!
RS
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May 27th, 2017 at 4:29:09 PM permalink
Quote: 100xOdds

New calcs (and using a $4k bankroll for all):
CE ($2 9/6 JoB)= -$0.46 - (($10*4.42)^2)/(2*.5*$4000) = -$.95
CE ($2 9/7 tdb) = -$.42 - (($10*9.91)^2)/(2*.5*$4000) = -$2.88
CE ($0.50 Multistrike (9/6 JoB)) = -$.21 - ($10*17.55)^2/(2*.5*$4000) = -$7.91

so lower variance is king and trumps return.
Thus plain old 9/6 JoB is the winner.

interesting enough, even with $100k bankroll, 9/6 JoB is still the winner but Multistrike came in 2nd by a hair.
so with enough bankroll, return will overcome variance.

edit:
does Kelly even matter since it's the same for all 3 games?


Kelly is (EV/Var)*BR...not sure how it'd be the same. But playing a game with a disadvantage, your optimal bet is $0.


Also, I don't think you're supposed to multiply the entire bet ($10) against the variance (17.55) for MS. I can't imagine a $10 bet having a -$7.91 CE. It makes a whole hell of a lot more sense if you use the $2.50 figure for a hand, not $10.
100xOdds
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May 27th, 2017 at 4:38:00 PM permalink
Quote: RS

Kelly is (EV/Var)*BR...not sure how it'd be the same. But playing a game with a disadvantage, your optimal bet is $0.


meant Kelly factor. (fixed my post above)
ce= EV-((bet size*Standard Deviation)^2)/(2*Kelly factory*BR)

or is it the same thing?
Last edited by: 100xOdds on May 27, 2017
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AxelWolf
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May 27th, 2017 at 8:55:13 PM permalink
Quote: Ibeatyouraces

Just be homeless and beg.

Humans can eliminate taxes of they wanted to. You can't eliminate death.

Give it time. Perhaps many many years from now you will be able to live "forever".

We were all born to early IMO.

Who knows, even just 50 to 100 years from now what we might find.
♪♪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♪♪
mamat
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May 28th, 2017 at 2:02:36 AM permalink
Quote: billryan

Most casinos seem to reward cashback in mailings at least partially for what you lose, so a person who has four sessions in a month of -1000,-1000,-1000, + 2700 will get much more cashback than someone who does -150, +200, -200,-150 even though in the end they each lost $300 for the month, and had the same coin in. Bigger losses seems to equal bigger mailings.
I know that doesn't answer your question but helps explain why a higher variance game is better, IF you are properly funded.

Some casino mailers are so heavily based on "Actual Win" rather than "Theo Win", that the same amount of play may generate $3,000-5,000/month or $40-200/month.
In some cases, 1% of the action with a small -$1K to -$2K loss ... is rewarded better than a win of any size.
Casinos can use both ADT and ADW (also PADT and PADW) in addition to total actual/theo win.

In these cases, it may be better to switch casinos after big winning/losing sessions, and only return the following month.
That way in your swings, you will have some casinos seeing large losses.

Casinos often target benefits ("player reinvestment") at 25-33% of Theo Win.
However some marketing departments are aggressive (or faulty), and it may be possible to receive 500-2000%+ of Theo Win by gaming the system.

Quote: FleaStiff

True, but mailings are frosting on the cake. A mailing is good, a really generous mailing is better, if MY mailing is better than YOURS I may feel that "I've won" against you. If my mailing is better than it otherwise would be, I may feel like "I've won" against the casino's computerized mailing program. Perhaps I have won against the casino's mailing program, but any way you look at it what really counts is what takes place in the casino.

So it takes a fully funded 'staying power' to be able to outlast that variance factor and receive the enhanced mailing.

Some people make 90-120% of their profits from mailers (I call them "back-end" players). Others make most of the profits up front ("front-end" players).

In my case, FP in mailers is about 15-20% of gross profits.
Last edited by: mamat on May 28, 2017
odiousgambit
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May 28th, 2017 at 2:53:45 AM permalink
Quote: AxelWolf

Give it time. Perhaps many many years from now you will be able to live "forever".

We were all born to early IMO.

Who knows, even just 50 to 100 years from now what we might find.



I do not wish to live in that time myself, check out my new signature line
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
TomG
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May 28th, 2017 at 3:19:56 PM permalink
Quote: 100xOdds

Is there a sweet spot or a rule of thumb for Return vs Variance when deciding on which game to play?



Edge or Expected Value, should always be the dominant factor. Only as bet size increase, does Variance become something that we need to consider if we are going to take on less value. For a $1.25 bet, I don't care at all about variance, all I care about is what is my edge; for a $100,000 bet I would care very much about possible variance. For a $10 bet, I don't care much about variance, but I also don't care much about 0.04%.

If you're not sure, one possible way to handle the situation is to assume that right now you are at the "break-even" point, where both games are equal. If money coming in from this point forward exceeds money going out, you play the higher variance. If money going out is greater, then you play lower variance
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