Optimum strategy for playing Bankroll through at Blackjack

Bringing my question here, where it should have been. Sorry.

I had a situation where I needed to wager through my £1000 bankroll through Blackjack 300 times over. Upon completion of that, whatever remains crystalises as withdrawable cash. Until wagered through it is non-withdrawable.

Now, by the seat of my pants and insane over-betting, I achieved that Other thread

My Math question is, what should I have done to balance ROR against the potential of withdrawing my bankroll, plus or minus a bit?

Actual maths or spreadsheets will be appreciated and may even be useful to future 'bonus users'

Thanks in advance to those who take the challenge.

I am assuming that you have £1000 that you can't touch until you play 300 hands.

In this case, my gut answer is, play the minimum for all 300 hands (although you do split and double when advantageous). Never mind about "the potential about withdrawing my bankroll." Don't raise the bets until it gets to the point where you can't possibly lose whatever the bankroll has become before you can withdraw it, at which point, bet it as if it's your money, because at that point, it is.

Quote: ThatDonGuy

I am assuming that you have £1000 that you can't touch until you play 300 hands..

Thanks. Not quite Don: It's not 300 bets, but it is £300,000 of total action.

I start out with £1000 of bonus credit (how I get to that point is a whole other story)
I wager from that 'bankroll' so my bonus balance goes up and down in line with my luck. Regardless of how high the balance goes, it's just bonus credit and all winnings are going back into the same pot. All losses are coming out of the same pot.

If I bust out completely, then that is the end of the bonus and I'd have to buy in just as a regular player: Real money in stays as real money.

If I wager through the starting bonus of £1000 300 times over, £300,000 in total action, then the casino converts what bonus balance that I have left, and all winnings, into real cash which I can withdraw... Which I actually have withdrawn :o)

Now. If I simply staked it as one massive bet of £1000, that would be one lot of my 300 play-throughs. If that won, I might double up, making 2 more of those play-throughs. I might then play £4000 bringing me to a total of 7 play-throughs. I think we can see that with HUGE bets like that, I could achieve play-through in a few hands (9 consecutive winning hands if we ignore Blackjacks). But that would leave me with a MASSIVE profit or nothing at all: A rather silly way of blowing my grand.

I could have rotated the money through at £1 a go, which would have needed 300,000 games. Expected loss on those games would be the order of £0.0055 per game, totalling -£1650.00 In other words I would probably be wasting a lot of time just to go bust.

My objective was no real profit, just survival.

I strongly suspect that there is a middle ground ideal betting level which could be worked out exactly with a bit of calculus, or by simulation. But, for now, I admit the maths is beyond me.

I did it in practice, almost on the button, checking out with £1050 of real money. I might have been out sooner and richer, but I hadn't been scrupulously following my own progress.

Somebody might want to show their mathematical prowess to solve this. Alan M and Evenbob need not apply :o)

Quote: OnceDear

My objective was no real profit, just survival.

I strongly suspect that there is a middle ground ideal betting level which could be worked out exactly with a bit of calculus, or by simulation. But, for now, I admit the maths is beyond me.

Don Schlesinger did just that in his trip risk of ruin formula
i thinks should do the trick for you

it can be found in his famous BJ book, qfit has it too
and MAYbe many other places (I have it in 2 Excel workbooks - One by Dunbar and the other Alan Krigman)
i think Alan's is in my online folder too

here is what i show

bet
# of rounds (these two should = 300,000)
and RoR

hope it helps out
==============
200
1,500
92.6362%

100
3,000
90.3899%

50
6,000
87.8220%

20
15,000
84.3327%

10
30,000
82.1718%

6
50,000
81.2268%

5
60,000
81.0794%

3
100,000
81.3263%

2
150,000
82.3077%

1
300000
85.6821%

i used -.005 edge and sd=1.14

Quote: mustangsally

...Here is what i show

10
30,000
82.1718%

6
50,000
81.2268%

5
60,000
81.0794%

3
100,000
81.3263%

Wow. thanks Sally. I'm about to DL your workbook. Much appreciated.

That calculator has really helped. So it looks like my best probability of surviving was about 1 in 5 and the optimum bet was in the order of 0.5% of bankroll.

I certainly didn't and wouldn't mess about playing 60,000 hands for a 1/5 chance of surviving. I was throwing £100 a bet most times, which would imply my chance of survival was more like 1/10.

I'm one lucky devil.

My way only took a couple of short sessions too.

Are you sure that isn't risk of ruin before doubling bankroll? It seems worse than I experienced. I never slipped below £800.

Thanks again.

Quote: OnceDear

Wow. thanks Sally. I'm about to DL your workbook. Much appreciated.

it is named
RoR - Alank
an Excel file

hope you can use it

i have a link to Alan's webpage some place where this was found
he passed away a few years ago and neveer did have his own web site
I wanted to change that but was too late

Quote: OnceDear

I'm one lucky devil.

me too
that makes at least 2 lucky devils
my husband is not one, but he needed no luck at all to catch me

Quote: mustangsally

that makes at least 2 lucky devils

Please don't use the expression 'At least' in a sentence with '2' in it, because for some reason it starts my nightmare again where I scream 'At least one of the dice is a two'

:o)

Quote: OnceDear

Please<snip>

:o)

yes, Alan M must be another lucky devil to have lived to be a senior, just thinking