Return vs Variance trade offs?
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?
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.
Quote: 100xOddsLets 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.
Quote: RSOne 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?
Quote: 100xOddsQuote: RSOne 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)
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. 'Quote: 100xOddsVariance of $2 9/6 Jacks or Better (99.54%): 19.51
Variance of $2 9/7 Triple double bonus (99.58%) : 98.28
Quote: RShttps://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?
Quote: odiousgambitI 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.
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.Quote: billryancasinos reward in mailings for what you lose, so Bigger losses equal bigger mailings.
So it takes a fully funded 'staying power' to be able to outlast that variance factor and receive the enhanced mailing.
Quote: 100xOddsthx.
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.Quote: RSQuote: 100xOddsthx.
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.
Quote: FleaStiffTrue, 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.
Quote: IbeatyouracesYou can't guarantee mailers either.
What can you guarantee?
Quote: billryanWhat can you guarantee?
Just death.
Quote: RSWhy 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 :)
Quote: IbeatyouracesJust death.
and taxes
Quote: rsactuaryand taxes
You can't guarantee that. Plenty of people that never pay taxes.
Quote: IbeatyouracesYou can't guarantee that. Plenty of people that never pay taxes.
Property tax, sales tax, tobacco tax, gas tax, etc. ?
Quote: RSProperty 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.
Quote: RSAlso, 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?
Quote: 100xOddsNew 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. :-)
Quote: 100xOddsNew 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.
Quote: RSKelly 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?
Give it time. Perhaps many many years from now you will be able to live "forever".Quote: IbeatyouracesJust be homeless and beg.
Humans can eliminate taxes of they wanted to. You can't eliminate death.
We were all born to early IMO.
Who knows, even just 50 to 100 years from now what we might find.
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.Quote: billryanMost 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.
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.
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).Quote: FleaStiffTrue, 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.
In my case, FP in mailers is about 15-20% of gross profits.
Quote: AxelWolfGive 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
Quote: 100xOddsIs 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
