Bankroll Management

[blackjack avenger]

Let's give some thought on how to manage a bankroll to suit one's goals.

given:
10g bank
Starting fixed ROR 13.53%

Goal
Max growth
method
Resize frequently bets upward with bank growth, do not resize downward with bank losses.

Goal
bankroll preservation
method
Resize frequently bets downward with bank loss, do not resize upward with bank growth.

Thoughts?

 

[zengrifter]

Let's give some thought on how to manage a bankroll to suit one's goals.

given:
10g bank
Starting fixed ROR 13.53%

Goal
Max growth
method
Resize frequently bets upward with bank growth, do not resize downward with bank losses.

Goal
bankroll preservation
method
Resize frequently bets downward with bank loss, do not resize upward with bank growth.

Thoughts?

Use growth and preservation strategies simultaneously. Resize at 50% points -
BR falls 50%, cut bet size to 50% - BR grows 50% increase bet size 50%. zg

 

[blackjack avenger]

Middlin

Zen
Looks like you found a middle strategy.
It is a little more aggressive then the double your bank or half it strategy.

I believe one would have a 75% chance of winning 50% of bank before losing 50% of bank.

Perhaps this can be called the "two face" betting strategy:whip:

 

[sagefr0g]

with ten grand i'd rather have a lower ROR.
maybe one percent. (not really sure)
to where your max bet doesn't get you in those really wild swings so much.
but yeah raise the max bet at some point as the roll grows.
it would be nice if you could start out with a unit that could be reduced if the roll declined to some point. just doubt with a ten grand roll that could be done with as low a ROR as i'd want.

actually i'd rather not have a bankroll at all except some modest trip bankroll.
have some 'reasonable' ramp and spread for that trip.
go at it like that each time while watching your bottom line. have the idea of when i've lost to much then screw it or if i'm winning money then good. if your winning money set it aside and consider it touchable if you want in the future for play purposes.
such is the life of a recreational player me thinks.

 

[blackjack avenger]

with ten grand i'd rather have a lower ROR.
maybe one percent. (not really sure)
to where your max bet doesn't get you in those really wild swings so much.
but yeah raise the max bet at some point as the roll grows.
it would be nice if you could start out with a unit that could be reduced if the roll declined to some point. just doubt with a ten grand roll that could be done with as low a ROR as i'd want.

actually i'd rather not have a bankroll at all except some modest trip bankroll.
have some 'reasonable' ramp and spread for that trip.
go at it like that each time while watching your bottom line. have the idea of when i've lost to much then screw it or if i'm winning money then good. if your winning money set it aside and consider it touchable if you want in the future for play purposes.
such is the life of a recreational player me thinks.

Well, I think you know you can have a fixed 1.83% ror or even 1%, but when exactly would you raise or lower your bets?

or

One could start of at a 13.53% fixed and if they lose half their bank and cut bets in half then their total ror I think is about 5%.

Which would you prefer? or something else?

 

[cardcounter0]

Resize frequently bets upward with bank growth, do not resize downward with bank losses.

Sounds like a recipe for going broke. Blackjack has it's ups and downs no matter what advantage you have. You swing up and resize to larger bets. Then when the down swing rolls around you lose it back faster. At break even you are now overbetting your bankroll. The down swing continues and you lose faster than ever, or you get another up swing and win it all back and go higher, so resize to a larger bet size and be prepared to lose it even quicker.

Normally 90% of the time you are behind. In other words, you have won more and lost a little back. It is rare to be at an all time high, you usually slide back a little. If you resize to bigger bets on every upstroke, then you are going to be continually overbetting -- which leads to going broke.

"one could start of at a 13.53% fixed and if they lose half their bank and cut bets in half"

Although this helps keep you from going broke, it is not a good way to make money. If you ever have a bad run and lose half, when you resize, it now takes you twice as long to dig yourself out of the hole. It will seem like you are always scratching your way out to get even.

Size your bets to your bankroll and a ROR % you are comfortable with. If you lose half your bank, dig out of the hole at the full bet rate and time (or go broke -- that is the risk you accepted when you started). If your bank increases enough (double, 80%, 150%), then resize. The initial ROR % is partially based on banking winnings and it anticipates that you might have a losing streak -- you don't want to increase bet size too soon or you are playing at a higher ROR % -- you lose it back faster than you bank it.

 

[sagefr0g]

Well, I think you know you can have a fixed 1.83% ror or even 1%, but when exactly would you raise or lower your bets? talkin some lifetime ror here for some arbitray lifetime bankroll.

not sure the significance of the 1.83% figure
but i'd just sim what ever game and adjust to the ROR i want and the sim sets up the proper betting proportion. then you know your winrate and can decide if your happy with that or not.

or

One could start of at a 13.53% fixed and if they lose half their bank and cut bets in half then their total ror I think is about 5%.

Which would you prefer? or something else?

isn't when your ROR is circa 13% your probably betting close to full kelly and thats likely optimal for your bankroll growth? thing is that's known to have 'scary' fluctuations for most mere mortals. to where i think it's common according to Snyder that one goes maybe 1/3 kelly and all that? so i doubt i'd wanna start at the 13.53% and then if i lost half the bank cut bets in half for the 5%.
so when you say a total ROR of 5% do you mean for that half a bank you got left or looking at the past history of once having had twice as much bank proclaim to yourself that prior bankroll now is being risked at 5% instead of 13.53%. sorry i'm total ignorant of how that works.

really i think i'd rather just go trip by trip maybe leave the worrying about some ROR to the trip bank instead of the lifetime deal. have some 'modest' goal and hope i make it. maybe just have some imaginary lifetime bankroll that seems maybe reasonable and some hoped for ROR for that imaginary lifetime bankroll. then just play as if the lifetime roll was real but going by some really trip bankroll with some 'reasonable' ror and goal. all the while keeping track of the bottom line money lost or won and maybe make decisions based on that about future play.
all that along recreational lines. but really i get pretty wild i guess with my fuzzy counting thing so even with all that i can only hope to be in the ballpark hopefully of all that. lol

 

[blackjack avenger]

Let's See What Mess I Get Into Now

not sure the significance of the 1.83% figure
but i'd just sim what ever game and adjust to the ROR i want and the sim sets up the proper betting proportion. then you know your winrate and can decide if your happy with that or not.

isn't when your ROR is circa 13% your probably betting close to full kelly and thats likely optimal for your bankroll growth? thing is that's known to have 'scary' fluctuations for most mere mortals. to where i think it's common according to Snyder that one goes maybe 1/3 kelly and all that? so i doubt i'd wanna start at the 13.53% and then if i lost half the bank cut bets in half for the 5%.
so when you say a total ROR of 5% do you mean for that half a bank you got left or looking at the past history of once having had twice as much bank proclaim to yourself that prior bankroll now is being risked at 5% instead of 13.53%. sorry i'm total ignorant of how that works.

really i think i'd rather just go trip by trip maybe leave the worrying about some ROR to the trip bank instead of the lifetime deal. have some 'modest' goal and hope i make it. maybe just have some imaginary lifetime bankroll that seems maybe reasonable and some hoped for ROR for that imaginary lifetime bankroll. then just play as if the lifetime roll was real but going by some really trip bankroll with some 'reasonable' ror and goal. all the while keeping track of the bottom line money lost or won and maybe make decisions based on that about future play.
all that along recreational lines. but really i get pretty wild i guess with my fuzzy counting thing so even with all that i can only hope to be in the ballpark hopefully of all that. lol

I believe the 5% ror is your total ror from the beginning when you decide to play the cut stakes in half style. One's chances of doubling before losing half I believe is 66%. If you lose half your stake and then cut your bets in half from that point forward if you do not resize again the ror should be 13.53%?

The 13.53% ror for fixed betting is not magical, not different from 14% or 10% except for the actual number. The 13.53% comes from what the fixed ror would be for optimal resizing. If you were to optimal resize at any one particular moment your ror should be 13.53%.

 

[sagefr0g]

I believe the 5% ror is your total ror from the beginning when you decide to play the cut stakes in half style. One's chances of doubling before losing half I believe is 66%. If you lose half your stake and then cut your bets in half from that point forward if you do not resize again the ror should be 13.53%?

thank you blackjack avenger. wow that's kind of cool.

The 13.53% ror for fixed betting is not magical, not different from 14% or 10% except for the actual number. The 13.53% comes from what the fixed ror would be for optimal resizing. If you were to optimal resize at any one particular moment your ror should be 13.53%.

lol it seems kind of magical to me.
no really maybe it's just me, my experience what i've seen messing around with sims.
just seems that 13% number or there close abouts pops up when you maximize your bankroll growth using a sim for some bankroll.
probably i'm wrong. seemed like i recall automonkey talking about how it's usually about 13% ror when your shooting for maximizing bankroll growth.
probably just a coincidence maybe.
i'll go fool with my simulator till i find some bankroll or what ever and the ror doesnt come close to 13%. that'll prove i'm wrong lol.:joker:
edit:ok yeah your right lol nothin magical. i just found a 7% ror for a maximize bankroll.

 

[blackjack avenger]

Is You Is Or Is You Ain't

thank you blackjack avenger. wow that's kind of cool.

lol it seems kind of magical to me.
no really maybe it's just me, my experience what i've seen messing around with sims.
just seems that 13% number or there close abouts pops up when you maximize your bankroll growth using a sim for some bankroll.
probably i'm wrong. seemed like i recall automonkey talking about how it's usually about 13% ror when your shooting for maximizing bankroll growth.
probably just a coincidence maybe.
i'll go fool with my simulator till i find some bankroll or what ever and the ror doesnt come close to 13%. that'll prove i'm wrong lol.:joker:
edit:ok yeah your right lol nothin magical. i just found a 7% ror for a maximize bankroll.

Can't your sim run optimal bets? Wouldn't that be the best? It should be 13.53% ror.

For fixed bets your ror is what it is, 10%, 13.53%, 15% whatever.

With optimal continuous resizing (kelly criterion hypothetical 0% ror,) if you were to take a snapshot ror for a moment in time, that ror is 13.53%. This is where the 13.53% comes from.

 

[sagefr0g]

Can't your sim run optimal bets? Wouldn't that be the best? It should be 13.53% ror.

For fixed bets your ror is what it is, 10%, 13.53%, 15% whatever.

With optimal continuous resizing (kelly criterion hypothetical 0% ror,) if you were to take a snapshot ror for a moment in time, that ror is 13.53%. This is where the 13.53% comes from.

below is a help screen for my cvcx program where the magical or not so magical number is mentioned circa 13% lol.
what ever in the world it means.

 

[Kasi]

not sure the significance of the 1.83% figure

All I think know is that is the ROR for a Kelly better betting half-Kelly. In other words the full-Kelly risk of .1353 times .1353 = .0183. So a quarter-Kelly better's ROR would be .0183*.0183. Now you can do it too lol. Understanding what it really means is another story.

But as to the rest of your excellent questions, I just don't quite know.

Kelly's goal is maximize growth rate of bankroll I think as opposed to the other goal of maximizing EV. Are these 2 completely incompatible goals?

"Pure Kelly" (maybe only playing one has an advantage?), "proportional betting Kelly" (the first and, in addition, bet is adjusted to size of current bankroll each time so one could never go broke?), " fixed Kelly betting" (is that when you even play some hands with a disadavanatge?), "continuous Kelly betting". (each bet will be based on original roll but the bet will change to always have the same max growth rate?).

If your goal is "Kelly", wouldn't that change maybe BS let alone traditional index numbers?

I don't know, I sort of think maybe a Kelly better would ahve a different unit roll in the first place than an EV-maximizing player since they have different goals?

 

[Kasi]

I believe the 5% ror is your total ror from the beginning when you decide to play the cut stakes in half style. One's chances of doubling before losing half I believe is 66%. If you lose half your stake and then cut your bets in half from that point forward if you do not resize again the ror should be 13.53%?

The 13.53% ror for fixed betting is not magical, not different from 14% or 10% except for the actual number. The 13.53% comes from what the fixed ror would be for optimal resizing. If you were to optimal resize at any one particular moment your ror should be 13.53%.

OK - like I think you are saying I would take the square root of the original 0.135 risk and get .3679 as to the chances of losing half your roll. Then I'd multiply that .36 by the original risk and get the 5% I think you are talking about and agree that at the point of re-sizing, from that point forward, your risk is the original .1353.

But, then, why, going back to your 0.78% of a quarter-Kelly bettor ever losing half his roll, (.5^7), why wouldn't it be the square root of 0.0335% or 1.8%?

I know your're going to say it has something to do with doubling your roll but I don't think so. But willing to listen of course.

Somebody give me a dull butter knife so I can slice my wrists :grin: :whip:

 

[blackjack avenger]

Yep

below is a help screen for my cvcx program where the magical or not so magical number is mentioned circa 13% lol.
what ever in the world it means.

I agree 100%, basically not different then what I stated.

At the bottom paragraph is mentioned .5 fixed Kelly, that is where I got the 1.83% ror I mentioned earlier, that is the ror for .5 fixed kelly.

 

[blackjack avenger]

Like a Dull Knife Through Butter

OK - like I think you are saying I would take the square root of the original 0.135 risk and get .3679 as to the chances of losing half your roll. Then I'd multiply that .36 by the original risk and get the 5% I think you are talking about and agree that at the point of re-sizing, from that point forward, your risk is the original .1353.

But, then, why, going back to your 0.78% of a quarter-Kelly bettor ever losing half his roll, (.5^7), why wouldn't it be the square root of 0.0335% or 1.8%?

I know your're going to say it has something to do with doubling your roll but I don't think so. But willing to listen of course.

Somebody give me a dull butter knife so I can slice my wrists :grin: :whip:

I don't have my material (sch.) with me that talks about using the square root of the original risk. So I am using some fuzzy memory:joker:

I address your thoughts in two? posts under (the movie 21 thread), hint, look for the :joker:

 

[sagefr0g]

.....
If your goal is "Kelly", wouldn't that change maybe BS let alone traditional index numbers?

since i'm completely lost i'll just quote the math prof

"......Strategy Changes

However this approach will not work with BlackJack. In BJ, the payoffs are determined by Players strategy and a Kelly player will not follow the conventional strategy when they have a large portion of their capital at risk. Standard BlackJack strategies are based upon maximizing expectation whereas Kelly strategies would maximize the expectation of logarithms. When only a small of capital is wagered, then the difference between these two strategies is negligible. However this breaks down when larger amounts are bet. For example, a Kelly player with a big bet out should insure "good hands" even if the expectation on the Insurance Bet were negative. (There is an excellent discussion of this point in the 1986 edition of Griffin's "Theory of BJ"). Similarly, Kelly strategy would dictate passing up many double down bets when the gain from doubling did not justify the increased risk. (Or, double down for less if allowed.)"
http://www.bjmath.com/bjmath/kelly/break.htm (Archive copy)

i'm so lost i'm begining to feel queezy.
thank goodness for cvcx gives me such a warm fuzzy feeling. :joker:

 

[blackjack avenger]

Nothing and Something

since i'm completely lost i'll just quote the math prof

"......Strategy Changes

However this approach will not work with BlackJack. In BJ, the payoffs are determined by Players strategy and a Kelly player will not follow the conventional strategy when they have a large portion of their capital at risk. Standard BlackJack strategies are based upon maximizing expectation whereas Kelly strategies would maximize the expectation of logarithms. When only a small of capital is wagered, then the difference between these two strategies is negligible. However this breaks down when larger amounts are bet. For example, a Kelly player with a big bet out should insure "good hands" even if the expectation on the Insurance Bet were negative. (There is an excellent discussion of this point in the 1986 edition of Griffin's "Theory of BJ"). Similarly, Kelly strategy would dictate passing up many double down bets when the gain from doubling did not justify the increased risk. (Or, double down for less if allowed.)"
http://www.bjmath.com/bjmath/kelly/break.htm (Archive copy)

i'm so lost i'm begining to feel queezy.
thank goodness for cvcx gives me such a warm fuzzy feeling. :joker:

As far as basic strategy changes based on the Kelly criterion. I don't know of any recomendations.

Risk Averse Indices - There is something to them.

 

[blackjack avenger]

Sooooo Situational

Resize frequently bets upward with bank growth, do not resize downward with bank losses.

Sounds like a recipe for going broke. Blackjack has it's ups and downs no matter what advantage you have. You swing up and resize to larger bets. Then when the down swing rolls around you lose it back faster. At break even you are now overbetting your bankroll. The down swing continues and you lose faster than ever, or you get another up swing and win it all back and go higher, so resize to a larger bet size and be prepared to lose it even quicker.

:joker:blackjack avenger
Of course your ror would go up vs fixed not resizing. However, here is a scenario where this strategy may have some benefit. One has the proper bank to play $5 tables, but the $10 game is better. As one wins enough for a session of $10 play they can play up and hope to stay. If they lose the session it's back to the $5 table. I would think they would get to the $10 game regularly sooner then if they wait to double their bank.

Normally 90% of the time you are behind. In other words, you have won more and lost a little back. It is rare to be at an all time high, you usually slide back a little. If you resize to bigger bets on every upstroke, then you are going to be continually overbetting -- which leads to going broke.

:joker:blackjack avenger
I think you are at an all time high about 1% of the time.

"one could start of at a 13.53% fixed and if they lose half their bank and cut bets in half"

Although this helps keep you from going broke, it is not a good way to make money. If you ever have a bad run and lose half, when you resize, it now takes you twice as long to dig yourself out of the hole. It will seem like you are always scratching your way out to get even.

:joker:blackjack avenger
You have a 66% chance of doubling before losing half.

Size your bets to your bankroll and a ROR % you are comfortable with. If you lose half your bank, dig out of the hole at the full bet rate and time (or go broke -- that is the risk you accepted when you started). If your bank increases enough (double, 80%, 150%), then resize. The initial ROR % is partially based on banking winnings and it anticipates that you might have a losing streak -- you don't want to increase bet size too soon or you are playing at a higher ROR % -- you lose it back faster than you bank it.

:joker:blackjack avenger
If you don't lose half your bank; only third of time, you can continue to play bigger bets. If you play with a fixed ror of 5% you are betting low at the outset. Why you would want to bet small from the beginning? because you may lose half and have to lower bets? Finally, it seems resizing is closer to optimal.

Once you double your bank your ror drops to 1.83%.
If you triple it your ror drops to .24%

When would you resize up?

 

[cardcounter0]

If you don't lose half your bank; only third of time, you can continue to play bigger bets.

That 1/3 of the time losing half your bank is based on not increasing your bets on the upswing. If you increase your bets on the upswing, then you will find yourself with 1/2 a bank more than 1/3 of the time.

If you play with a fixed ror of 5% you are betting low at the outset.

Although 5% ROR sounds low, playing professionally, it is very risky. 5% means 1 of 20 times, it will happen!

If you are playing with a fixed bank and drawing off your expenses or profits, then sooner or later your 20:1 shot is going to hit and you are broke. If you are doubling a bank every 3 or 4 months, than you might find yourself begging for quarters in the street in less than 5 years.

 

[blackjack avenger]

Different Scenarios

If you don't lose half your bank; only third of time, you can continue to play bigger bets.

That 1/3 of the time losing half your bank is based on not increasing your bets on the upswing. If you increase your bets on the upswing, then you will find yourself with 1/2 a bank more than 1/3 of the time.

:joker:blackjack avenger
Yes, I agree. I was talking about your section where you mention not resizing with a 5% ror vs resizing if half bank is lost. If you do not resize you double bank before losing half 66% of time.

If you play with a fixed ror of 5% you are betting low at the outset.

Although 5% ROR sounds low, playing professionally, it is very risky. 5% means 1 of 20 times, it will happen!

:joker:blackjack avenger
Yes, I agree again, 5% may be to risky for some. The 5% was an example if you are willing to cut to half stakes if half of bank is lost. It does point out that if one cuts their bets at some point they can potentially play bigger longer and still have a low ROR. If you want to play with a fixed 1% ror then you would be betting even smaller vs some sort of resizing on losses plan.

If you are playing with a fixed bank and drawing off your expenses or profits, then sooner or later your 20:1 shot is going to hit and you are broke. If you are doubling a bank every 3 or 4 months, than you might find yourself begging for quarters in the street in less than 5 years.

:joker:blackjack avenger
Yes, I agree again, but we have not touched on expenses or taking out profits. Also, it's easy to drop below 5% ror by cutting bets if your bank drops again.