Unit betting porabla and the 'safest positive return'

I am delurking for a post, I am not exactly sure what Im trying to find out on this post, BUUUT

OK- so betting in 'units' - I am noticing a porabla at where the additional unit is adding to your bankroll more then if you increased your unit staked.

if you start off with 100 units and bet 1 unit and win and then bet 2 units, your now staking almost twice as much as your original unit (closer to 2% of your funds vs the 1% of the original bet.)

but as this keeps going, there is a point at which your winning causes your next bet to be a lesser percent of your total bankroll (after the last win). What is that point?

If I bet all 100 units and win, I would now be betting 101 units out of 200 or taking my risk down to almost half. If I bet 10 units and win Id have 110 and risking 11 which remains 10% from bet to bet. if I risk 8 of 100 (8%) and win I then risk 9 out of 108 (8.33%)

If I risk 11 units of 100 and win then risk 12 out of 111, my risk goes down to 10.8%

And this is the point I start to see a difference- risking right at 11% of the initial stack to actually ADD to your stack before the next bet is increased.

But why? - If I was to consider both sides of this 'porabla' I see- I would want to say that if you were trying to find your way between risk and reward, and trying to up your reward without too big an increase in risk - then this little "11%" area is where youd be most comfortable.

Looking for thoughts on the topic- sorry if this is a dead horse of a subject. My idea isnt looking for an increasing betting system, but to study why this porabla effect happens and how to take advantage of this point in the betting axis.

First of all, when you say "porabla", do you mean, parabola?

Anyway, your problem seems simple enough: given bankroll B, for what bet X does the percentage of bankroll bet reduce if you win and then bet X+1?

The first bet fraction is X / B; the second bet fraction is (X + 1) / (B + X)
X / B > (X + 1) / (B + X) when X (B + X) > B (X + 1) -> XB + X² > XB + B -> X² > B
The percentage goes down when the first bet is greater than the square root of the initial bankroll

I do notice, however, that you are expressing "risk" in terms of the percentage of your bankroll. $100 is $100, whether it's part of a $100 bankroll or a $10,000 one.

Quote:

@TheDonGuy Parabola = POWER

I have read that if u want to have 5% risk of ruin you should bet 36 units x hour, with 10% risk of ruin 30 units x hour 20% risk of ruin 26 units x hour and so on,....

but if u were a trader like myself, we use a formula for money management on how to calculate your contracts in relation to ur starting capital, here it is:

Starting capital + ( number of contract x 500 or 5000 depending on your capital)
explaining until you have reached $10000 you should use x500
after reaching 10k staring capital, u should do the x5000

example
starting capital $100 contract 1 = $1 betting you should bet $2 when your capital reaches
100+(1*500) = $600 at $600 u can increase ur betting by $2 and so on for $3 u should have:
100+(2=number of contract=ur betting size*500)= $1600 when u reach $1600 u can start betting $3

at $10000 u should increase *5000 and therefore getting

staring capital 10000 contract 10 = $10 u should bet $20 at $60000
10000+(10*5000) = $60000

at 100k starting capital is *50000 not *5000
at 1Mil starting capital is *500000

u can modify the contracts x ur likings but remember to never use more than 25% of ur starting capital, to define ur betting size

Quote: MGBJK

I have read that if u want to have 5% risk of ruin you should bet 36 units x hour, with 10% risk of ruin 30 units x hour 20% risk of ruin 26 units x hour and so on,....

Dunno where you read that, but it strikes me as nothing like a risk of ruin formula

Quote:

but if u were a trader like myself, we use a formula for money management on how to calculate your contracts in relation to ur starting capital, here it is:

Starting capital + ( number of contract x 500 or 5000 depending on your capital)
explaining until you have reached $10000 you should use x500
after reaching 10k staring capital, u should do the x5000

Sorry MG. I can do maths, but this isn't it.

Quote:

example
starting capital $100 contract 1 = $1 betting you should bet $2 when your capital reaches
100+(1*500) = $600 at $600 u can increase ur betting by $2 and so on for $3 u should have:
100+(2=number of contract=ur betting size*500)= $1600 when u reach $1600 u can start betting $3

at $10000 u should increase *5000 and therefore getting

staring capital 10000 contract 10 = $10 u should bet $20 at $60000
10000+(10*5000) = $60000

at 100k starting capital is *50000 not *5000
at 1Mil starting capital is *500000

u can modify the contracts x ur likings but remember to never use more than 25% of ur starting capital, to define ur betting size

I can do a little bit of English comprehension too. But again, this isn't it.
I guess that you are trying to be helpful, but please consider re-writing your post in a language that has meaning to your audience. The above is gibberish. Sorry.

@OnceDear Thank u for ur reply,

Quote:

Dunno where you read that, but it strikes me as nothing like a risk of ruin formula

5% risk of ruin you should bet 36 comes form the Bootlegger's 200 Proof Blackjack
Starting capital + ( number of contract x 500 or 5000 depending on your capital) is a trading formula that u can apply to blackjack to minimize risks.

Quote:

The above is gibberish.

You don't need it...., u should stick to what u do best, which is hating what other people write, good for you then!!!!!

Quote: MGBJK

@OnceDear Thank u for ur reply,

Quote:

Dunno where you read that, but it strikes me as nothing like a risk of ruin formula

5% risk of ruin you should bet 36 comes form the Bootlegger's 200 Proof Blackjack
Starting capital + ( number of contract x 500 or 5000 depending on your capital) is a trading formula that u can apply to blackjack to minimize risks.

Quote:

The above is gibberish.

You don't need it...., u should stick to what u do best, which is hating what other people write, good for you then!!!!!

MGBJK,

Thanks for quoting the source. I'll go and get a copy.

I tried to understand your post, much as any eager student of the subject might. But I failed grasp it and indicated to you that it was beyond my ability to comprehend. That might have been my poor learning skills or your poor explaining skills.

I didn't hate it.

I wanted to love it.

Your risk of ruin numbers may be a perfectly valid quote from that source doc, but lacked context. Without consideration of bankroll size, they lacked validity.

No need for the anger or attitude, MGBJK. I didn't intend to offend you, just as I'm sure you never intended to offend anyone here.

This is a forum where the logic and maths associated with betting are really cared about: It's a maths centric place where formulae are occasionally discussed, generally in English or American English. But there are pragmatists here who might correct things like the spelling of 'parabola' and 'you', or might ask how a formula works when it is not clear.

@OnceDear ok, apology accepted,...:-) let's start over, i am used to speak with traders so we communicate by our internal dialogue, sometimes I do forget that we are not speaking with the same structure, I indeed do like the logic, that is why I have joined this forum, ok let me clarify the formula, at the firm we arrived at the conclusion of getting the maximization of contracts based on our starting capital. In this way we wouldn't loose money based on a single trading size contract, but u could apply the fluctuation of the currency to the fluctuation + /- of the blackjack in terms of winning s vs looses,.... to be continued,........

the concept is really simple:
if u take our trading formula Starting capital + ( number of contract x 500 )
where 500 is related to your starting capital.
Your staring capital is your bankroll.
If u start with less than 10k u should use x500 because ur starting capital isn't enough to be playing at the big tables, so hypothetically:
Starting capital = $100
Number of contracts = your min bet size which in this case is $1
Min bet size = $1
U must use a flat betting system of $1 for each hands u'll be playing
Now the formula,:
Starting capital + ( number of contract x 500 )
$100x($1*500) = $600
Remember the bet used is for this particular example u can adjust the betting size and stick to the 25% of your starting capital, as a general rule.
When u have reached $600 it is the time to increase your betting size, to $2

To be continued,......

Now that u have increased the betting size to $2 u must adjust the formula
Starting capital + ( number of contract x 500) accordingly:
$100+($2x500) = $1600
Every time u reach a new step like in this case $1600 u must change the betting size to $3 and adjust the formula accordingly.
$100+($3x500) =.......... and so on, this will give you a new step where u will be increasing your betting size to 4
When u reach the 10k of your starting capital which is your bankroll, u must multiply the 500 in the formula x 10 so 500x10=5000 and adjust the formula accordingly.
Starting capital + ( number of contract x 5000)
When u reach 100k multiply 5000 x 10
When u reach 1mil multiply 50000 x 10
That's it!!!!!
Every time u increase your flat betting size by a +1 when reaching specific targets given by the formula, in this way you will be minimizing the risks of loosing your bankroll in the long term, and u will be knowing exactly how much to bet based on your starting bankroll, now if it is still gibberish,.....:-) well I am the one that's gonna say sorry!!!!!!!,........LOL

Quote: MGBJK

...now if it is still gibberish,.....:-) well I am the one that's gonna say sorry!!!!!!!,........LOL

Thanks for explaining further. I can't say that was totally clear to me, but then again it is late here and I've been drinking :o)
I have a first impression, but will read through again several times and see if I can fully understand your formulae before commenting further.
For now, I recommend that you search out member 'Romes' A-Z articles, especially his comments on Kelly Criteria and ROR. . .

https://wizardofvegas.com/articles/A-to-Z-Counting-Cards-in-Blackjack/

Quote: OnceDear

Thanks for explaining further. I can't say that was totally clear to me, but then again it is late here and I've been drinking :o)
I have a first impression, but will read through again several times and see if I can fully understand your formulae before commenting further.
For now, I recommend that you search out member 'Romes' A-Z articles, especially his comments on Kelly Criteria and ROR. . .

/articles/A-to-Z-Counting-Cards-in-Blackjack/

thank you,it is good for me ...
...
...