Bankroll. Time to double bankroll?

[junior_counter]

How long has it taken to double your bankroll(s)? First bankroll? Bankroll after gaining a bit more experience? I’m basing my bankroll on 500 times the base unit, or 100 times max unit, 1-5 spread. I plan on upgrading from red to green, once my bank has doubled and to me, proven success.

I'm estimating it will take ~500 hours with a 1-5 spread? I know this spread is probably too low, as indicated in a previous post.

How would you properly define bankroll in terms of units? Is the 500X base unit, 100X max unit above thinking correct?

Thanks in advance. JrC.

 

[assume_R]

How would you properly define bankroll in terms of units? Is the 500X base unit, 100X max unit above thinking correct?

I'll let some others answer your actual question, but regarding how to define a bankroll, whatever money you're truly willing to wager is your bankroll. If you would stop playing BJ if you happened to lose $4,000, then that's your bankroll. If you would lose $25,000 then take out a loan for another $25,000 then your bankroll is $50,000. And remember, Kelly betting says to tone down your unit size when you are in a downswing and ramp up your unit size when you're in an upswing!

 

[moo321]

There's no way to answer your question without more specifics. What game are you playing, at what counts will you hit what bet amount, will you wong out, back-count, is this a shoe, pitch, H17 S17, LS, penetration?

It literally could take anywhere from 30 to 10,000 hours to double a bank depending on these factors.

 

[NightStalker]

Based on the risk

my AVG ev is 0.15% of my BR wth 1%RoR, so 750hour would IDEALLY double it..
But i got my first double in 250hours and waiting for second double and it's over 750hours..

 

[blackjack avenger]

Not So Hard?

take your bank and divide by hourly EV = hrs to double.
This does not take into consideration the variance.
this is for fixed bets

:joker::whip:

 

[ycming]

I'll let some others answer your actual question, but regarding how to define a bankroll, whatever money you're truly willing to wager is your bankroll. If you would stop playing BJ if you happened to lose $4,000, then that's your bankroll. If you would lose $25,000 then take out a loan for another $25,000 then your bankroll is $50,000. And remember, Kelly betting says to tone down your unit size when you are in a downswing and ramp up your unit size when you're in an upswing!

Have you got any more link on:
"And remember, Kelly betting says to tone down your unit size when you are in a downswing and ramp up your unit size when you're in an upswing!"

Thanks
Ming

 

[Syph]

Hey JC,

Generally speaking, assuming you are playing a game with a $50 SCORE (the minimum, playable game ... according to some), you'll need about 20,000 hands for your EV to equal your bankroll. That's playing Full-Kelly (ie, betting ~1% of your bankroll with a 1% edge). With 100 maximum bets you are playing approximately 1/2 Kelly. Thus, you will require about 40,000 hands.

Now, this is simply expectation. Unfortunately, expectation and reality tend to diverge over the short-term. While you may be expected to double your bankroll in 40,000 hands, the reality is you only have a varying degree of probability to actually do so. The longer you play, the greater the probability of seeing your expectation. After 40,000 hands, playing off a Half-Kelly bankroll, you have about a 66.7% chance of actually doubling your bankroll. Most would consider this to be a bit uncertain. If you want a 95% certainty, you will have to quadruple this number to 160,000 hands. And if you want a 99.7% probability, you will have to multiply the number ninefold to 360,000 hands.

Most are happy with a 95% certainty. So for our 1/2 Kelly player ... about 1,600 hours to double the bankroll. This assumes you are playing a game with a $50 SCORE, and 100 hands per hour. Most counters are nowhere near that. However, if you are red-chipping, you should be able to find games with about a $100 SCORE, and can chop all these numbers in half.

That said, for a low stakes grinder, I think you'll find short-stacking the live $1/$2 NL poker cash games to have a much higher rate of return, with less variance. Find about three poker rooms and alternate them throughout the night. Double, leave, double, leave. Repeat as necessary. 6 pm to about 6 am. This is systematic ratholing and not looked upon too favorably, however there is little anyone can do to stop you.

Expect some hate.

And that should be the first indication you are doing something right.



Best,
Syph

 

[assume_R]

Have you got any more link on:
"And remember, Kelly betting says to tone down your unit size when you are in a downswing and ramp up your unit size when you're in an upswing!"

Thanks
Ming

Ming,

Let me explain the reasoning first, and if you'd like I can try to find some links on it if you still want afterwards.

Essentially, in its purest form, Kelly betting says to bet 2% of your bankroll with a 2% advantage (which, let's say, happens at TC +5). So if you have a $10k bankroll, you'd bet $200 at TC = +5. If you end up having a downswing, your bankroll might go down to $5k. At this point, when the TC is +5, you'd bet 2% of your bankroll, or $100. Now let's say you hit an upswing and your bankroll goes up to $15k. At this point, when the TC is +5, you'd bet 2% of your bankroll, or $300.

The numbers could be more exact if you took into account variance, possibly betting fractional Kelly, and the fact that you're forced to play -EV hands. But the principle will remain that your bet size will change as your bankroll fluctuates in terms of Kelly betting.

In math terms, Kelly betting will maximize the logarithmic growth of your bankroll, so you're not overbetting when your bankroll can't sustain it, and not underbetting when you have more money to place at risk.

Does that sufficiently answer your question logically or do you want me to find some additional references?

 

[blackjack avenger]

Kelly and EV

Let's say you have a SCORE of $40
If you bet kelly continuous (or near so) resizing your EV will be about $20 an hour.
If you bet half kelly continuous (or near so) resizing your EV will be about $15 an hour.

If you cut your bets on losses it cuts your EV, but your ror is greatly reduced.

 

[blackjack avenger]

For Fixed Kelly?

Hey JC,

Generally speaking, assuming you are playing a game with a $50 SCORE (the minimum, playable game ... according to some), you'll need about 20,000 hands for your EV to equal your bankroll. That's playing Full-Kelly (ie, betting ~1% of your bankroll with a 1% edge). With 100 maximum bets you are playing approximately 1/2 Kelly. Thus, you will require about 40,000 hands.

Now, this is simply expectation. Unfortunately, expectation and reality tend to diverge over the short-term. While you may be expected to double your bankroll in 40,000 hands, the reality is you only have a varying degree of probability to actually do so. The longer you play, the greater the probability of seeing your expectation. After 40,000 hands, playing off a Half-Kelly bankroll, you have about a 66.7% chance of actually doubling your bankroll. Most would consider this to be a bit uncertain. If you want a 95% certainty, you will have to quadruple this number to 160,000 hands. And if you want a 99.7% probability, you will have to quadruple this number as well to 640,000 hands.

Most are happy with a 95% certainty. So for our 1/2 Kelly player ... about 1,600 hours to double the bankroll. This assumes you are playing a game with a $50 SCORE, and 100 hands per hour. Most counters are nowhere near that. However, if you are red-chipping, you should be able to find games with about a $100 SCORE, and can chop all these numbers in half.

That said, for a low stakes grinder, I think you'll find short-stacking the live $1/$2 NL poker cash games to have a much higher rate of return, with less variance. Find about three poker rooms and alternate them throughout the night. Double, leave, double, leave. Repeat as necessary. 6 pm to about 6 am. This is systematic ratholing and not looked upon too favorably, however there is little anyone can do to stop you.

Expect some hate.

And that should be the first indication you are doing something right.



Best,
Syph

For fixed Kelly betting right Syph?

 

[Syph]

For fixed Kelly betting right Syph?

Bingo. Fixed-Kelly betting ... hold on. I just made a mistake. To cover 3SD (99.7% certainty), the Fixed-better should multiply his hands by 9, not 16. I'll edit this in the above. The numbers should be:

66.7% certainty: 20,000 hands
95% certainty: 80,000 hands
99.7% certainty: 180,000 hands

And double this if you were using a Half-Kelly initial bet-sizing approach.

The True-Kelly better, one who re-sizes his bets based on his bankroll, the following hands will be required (based on a $50 SCORE or 20,000 N0):

66.7 % certainty: 80,000 hands
95% certainty: 320,000 hands
99.7% certainty: 720,000 hands

Thanks, BA, for bringing this to my attention.

For those new, the Fixed-Kelly better is one who sizes his wagers to his initial bankroll size, and does not change his bet size as his bankroll fluctuates. The True-Kelly bettor always bases his wagers on the size of his bankroll.

Best,
Syph

 

[moo321]

Let's say you have a SCORE of $40
If you bet kelly continuous (or near so) resizing your EV will be about $20 an hour.
If you bet half kelly continuous (or near so) resizing your EV will be about $15 an hour.

If you cut your bets on losses it cuts your EV, but your ror is greatly reduced.

Assuming a 10k bank.