Turnover Till Broke Calculation Question

[Fizzer]

I am seeking a formula to calculate how much a punter will turnover until going broke given a specified starting bank and betting conditions. Let me further explain.

Our punter starts with a bank of $1,000. He is repeatedly offered 1.95 on the flip of a fair coin. He will pay a 7.5% commission on winnings. He will religiously bet 10% of his diminishing bank on each wager except the minimum bet is $20.

If I was inclined I could work this out with a pencil. But I am not so inclined and am sure a formula is out there and perhaps some software that allows one to input parameters and push a button.

Any takers please?

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[pantsdown]

http://www.puntingace.com/bettingdownlo ... lation.htm

[Fizzer]

http://www.puntingace.com/bettingdownloads/bettingsimulation.htm

Thanks pants - doesn't tell me exactly what I want to know but it can steer you in the right direction. Basically gave a best guess answer given that there can never be 'one' answer generated.

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[mistermac]

You are losing just over 6% of each dollar long term no matter what the staking plan using your figures. Therefore you will eventually lose your bank.

You have $1000 to go down the gurgler, and on average that will be gone in just over $16500 turnover.

However, there is massive variance in the way you lose your $1000 each time.

In 4 of ten cases on average, you will see you bank never go above the original $1000 with your staking plan.

But, there are two dead set certainties, you will lose your bank eventually, and the number of paths that loss will go are many, due to variance.

[Fizzer]

You have $1000 to go down the gurgler, and on average that will be gone in just over $16500 turnover.

Without going into minute detail mm how did you compute that, and to what degree of confidence can I place on your obviously higher wisdom?

I am attempting to put together a business plan for a mooted POS BetFair (white label) retail operation (TAB clone) and need to get a handle on some estimates.

If punter Joe Average brings $1000 to the table I am wanting to know how much money can be made from his turnover given I will net 2% of his winnings.

Thanks kindly.

My guesstimate is that if the POS operator nets 2% of paid winnings then he will net a little under 1% of gross sales. Be interesting see theory matched with reality.

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[mistermac]

You have $1000 to go down the gurgler, and on average that will be gone in just over $16500 turnover.

Without going into minute detail mm how did you compute that, and to what degree of confidence can I place on your obviously higher wisdom?

OK, Fizzer.

Common sense will tell us that our punter is on a loser, if only because he gets back $1.95 on his successful bets, whereas he needs $2 to be even with the game. He thus loses 2.5% by that fact alone long term.

Then, he is asked, if I read you right, to cough up 7.5% of $0.95 cents out of every $1 worth of winning bet. Now he wins with an "unbiased coin" long term one half of his wagers. 7.5% of 95 cents is 7.125 cents for every outlay of $2 long term, which makes 3.5725% of his outlays.

2.5% plus 3.5725% is 6.0725%.

So he has $1000 to lose over a series of bets which he will lose all but some amount of less than $20 left so that he cannot fund his minimum bet any longer.

So, what is $1000 6.0725% of? Roughly about $16500 which is my figure.

Admittedly, the road may have been up and down. long or short, but on average, it stands to reason that he will get $16500 worth of action.

The Greeks faced a similar problem when they debated whether the hare would ever catch up with tortoise. If I recall, it is called Zeno's Paradox, which is worth Googling to read about it, as many punters have wooly ideas because they have never heard or Zeno. He is jus a Zero on the radar.

Born nerd that I am, I am sorry if I have made your brain spin, but really it is just common sense what I say.

[mistermac]

Fizzer said:

If punter Joe Average brings $1000 to the table I am wanting to know how much money can be made from his turnover given I will net 2% of his winnings.

About $150 on average if my figures are correct, Fizzer.

Or have I misunderstood something?

[Fizzer]

Fizzer said:

If punter Joe Average brings $1000 to the table I am wanting to know how much money can be made from his turnover given I will net 2% of his winnings.

About $150 on average if my figures are correct, Fizzer.

Or have I misunderstood something?

It's a strange situation given the way the 'juice' is levied ie on winnings (forgetting the >100% market atm).

But in my scenario originally portrayed one might come at it from a different perspective. Since the punter has $1,000 to lose then he will eventually lose a maximum of $1,000. So who gets what proportion of the $1,000?

We know he loses 6% on TO (equates to return of $1.8 . The vig is shared thus:

1. the market >100% (ie $1.95) = 2.5%
2. 7.5% of winnings (2% is mine) = 3.5%

So I got approximately 1/4 of 3.5% of the total LoT 6% (=$1,000).

Sooooo.......I think 1/6 of the original $1,000 will be mine eventually which is .........about $160. How much did you say again? $150 - we're on the same page.

In the real world things of course have to be different because the smarter punters you have as customers the more money you will make relative to an outlet that hosts dumb punters. The smarties will bet/win more, the dummies will necessarily bet/win less.

The budding BetFair POS operator will want to nurture and attract smarties - not dummies as his customer base.

Thanks for your assistance mm.

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[jfc++]

Fizzer your calculations are way too complicated. MM is ~right.

The essential calculations of expectations possibly follow:

12.125% = Rake on Winnings

6.0625% = LOT

$990 = Target Loss

$16,329.9 = Action

$8,164.95 = Action on Winners

$7,669.95 = Payout on Winners

$153.40 = 2% of Winnings

As sequence termination is ~equally likely on any any amount below $20 that averages to $10 leading to my $990 target.

MM's alternate target of $980 results in $151.85.

[ixlat0]

Mistermac and jfc++ your common sense logic slipped along the way causing your calculations to be way off the mark -- AND (forgetting that your calculations were wrong) it is incorrect to add the 2.5% and 3.5% as you did (for an explanation look up Simpson’s paradox)

Fizzer -- i find your logical approach more intuitive -- however, your calculations are incorrect


OK -- the average ROI on $1,000 wagered (based on a market of 102.5%) = 1,000 x 0.975 = $975 which is subject to a 7.5% commission = 975 x 0.925 = $901.875
So TOTAL loss = 1000 – 901.875 = $98.125 comprising $25 (2.5% market) + $73.125 (7.5%commission)

The POS operator gets a 2% commission share of the 7.5% = 73.125 / 7.5 x 2 = $19.50

Therefore, POS operator % of total money lost is simply 19.5 / 98.125 = 19.87%

So if $1,000 lost then POS operator gets = 1,000 x 19.87% = $198.70

Mistermac tried going about it this way…

After calculating the $ amount lost (see above)

Total % loss from $1,000 wagered = 98.125 / 1000 = 9.8125%

Therefore, if 1,000 lost then total wagered = 1000 / 9.8125 x 100 = $10,191

Now if POS operator gets $19.5 per 1,000 wagered the he gets 19.5 x 10.191 = $198.70

[jfc++]

OK -- the average ROI on $1,000 wagered (based on a market of 102.5%) = 1,000 x 0.975 = $975 which is subject to a 7.5% commission = 975 x 0.925 = $901.875

You are applying 7.5% commission to something other than winnings.

Therefore you are wrong.

[ixlat0]

jfc++ i know where you're coming from and take your point -- but i clearly set things out that way bcoz that's the way i understood the problem -- i have also clearly set out the workings (either way) -- Fizzer has all he needs to recalculate if necessary

thx for your comment

[jfc++]

We know he loses 6% on TO (equates to return of $1.8 . The vig is shared thus:

1. the market >100% (ie $1.95) = 2.5%
2. 7.5% of winnings (2% is mine) = 3.5%


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Here is how the vig is really shared on 1 unit of winnings:

5% Betfair

Then from the remaining 95%

2% Fizzer
5.5% Middle Man

Or from 100%

5% Betfair
1.9% Fizzer
4.75% Middle Man

12.125% Total

So total player losses will be shared thus:

41.2371% Betfair
15.6701% Fizzer
43.0928% Middle Man


For the record, half of 7.5% is not 3.5%.

[jfc++]

Mistermac and jfc++ your common sense logic slipped along the way causing your calculations to be way off the mark -- AND (forgetting that your calculations were wrong) it is incorrect to add the 2.5% and 3.5% as you did (for an explanation look up Simpson’s paradox)

I correctly calculated a LOT of 6.0625%.

MM miscalculated it as 6.0725%.

But, as neither of those happen to be 6%, why accuse us of adding 2.5% and 3.5%!

3.5% is a blatant error, so why even mention that!

Simpson's Paradox generalises the memorable phenomenon where A can have a superior batting average over B in each of 2 seasons, yet an inferior one over those combined seasons.

In no way, shape or form does this have any relevance to this vig problem, so what possessed you name drop it here!

[mistermac]

Thanks, jfc+, for your help, and for pointing out my 6.0725 error .
Also, I had never heard of Simpson's Paradox. I had mentioned Zeno's P in an earlier post, so perhaps Ixl was trying to get one of his own in. But Zeno's refers essentially to the problem of an infinite series of decreasing terms, which causes a lot of confusion to some people. The hare "never" catches up to the tortoise, so they think.

BTW, I respect your grasp of Math, (if not your sometimes crusty manner), as even though I am not bad at it, I am not a Professional Mathematician. However, I reckon I am good at analysing and solving problems, as I was a Systems Analyst, and problem shooter in the halcyon days of programming. But, all the Wage, Tax, Superannuation, Local Body, and Billing programs that needed writing have been written years ago, and still creak along. They would cost megabucks to replace.

I am butting out of this Fizzer problem, therefore, now as you have a handle on it.

I hope Fizzer is happy with our combined effort.