One-Time-Only betting opportunity – how much do you bet?

Agree with catfloppo.

in theory:

4900 on singles
600 on doubles
76 on trebles
9.50 on quadruples
1.20 on quintuples
10p on sextuples(!?)

I also think in the absence of multiples I would bet about 11k per die... or am I out by a decimal point somewhere i haven't seen?

1k per die too. Any results can occur over 8 bets at 3.0, quite easy to lose the lot of them over such a short run, 33% value or not. If the offer was infinite I would be filling my boots though :)

ok Martinch, good man. You think Catfloppo, Trevh and Dave are being big girl's blouses for only betting £8k, and not exploiting the chance to do multiples?

formatted

Wins|Probability|P&L|bank

0|3.9%|-£61,023|£38,977

1|15.6%|-£41,536|£58,464

2|27.3%|-£12,305|£87,695

3|27.3%|£31,541|£131,541

4|17.1%|£97,303|£197,303

5|6.8%|£195,946|£295,946

6|1.7%|£343,731|£443,731

7|0.2%|£564,267|£664,267

8|0.0%|£890,971|£990,971

Wins	Probability	P&L	bank
0	3.9%	-£61,023	£38,977
1	15.6%	-£41,536	£58,464
2	27.3%	-£12,305	£87,695
3	27.3%	£31,541	£131,541
4	17.1%	£97,303	£197,303
5	6.8%	£195,946	£295,946
6	1.7%	£343,731	£443,731
7	0.2%	£564,267	£664,267
8	0.0%	£890,971	£990,971

I wouldn't have wasteD such an opportunity betting on singles.

2500 on each double.
  500 on each treble.
  114 on each treble.

A total of 106 k, so 6k is taken from savings.

If one or zero comes in, you would have 4 k to live on before you started in that job paying 2.5 k a month.

If two comes in you would have 40 k betting bank left,just enough to keeep on gambling and making at least 2 k per month.

If three comes in you will have made a net profit of 46 k.

If four or more comes in - HAPPY DAYS !!

Madness

I would theoretically bet on the 7 and 8 fold. just a number less than a penny. that's why I left it out.

Martinch - Our reckless bookie will take any size of stake, so less than a penny for 7's and 8 is fine (and yes he will pay). How did you generate your bet unit stakes if you don't mind me asking? And why do I get £32 less (£60,991) for your total stake?

By the way, I think it's much better to pay yourself a fixed amount each month, regardless of PnL, that way you don't need to keep capital sitting idly in the form of 'savings'.

imps, don't worry about the £32 - there are going to be rounding errors in it.  I had a closer look and I would bet 2.76p on each 7 fold.  I can't get a stake for 8 folds at the moment (it's really really small) but I know it exists.

I did all this in a spreadsheet using binomial distribution, kelly and solver.

here - this can probably explain better than I can (just remember decimal odds=4)

http://www.sbrforum.com/betting-tools/kelly-calculator/

my stakes were full kelly stakes, which is definitely the max one should risk, and is kind of short sited and takes no account of real life.

OVERBETTING ALERT!

It's a funny old thing risk, some people would risk their life savings on a single flip of a coin if the odds were say 3/1, a 50/50 chance of bust or quadrupling their worth.

Personally I play it very safe on here, I'm not tempted to over stake from my methodical plan and have no delusions of grandeur, am not greedy, am very content with the amounts that I make here, so increasing my risk on the 8 throws above is a no no as a one off event, attractive as it sounds.

Interesting to see the risk takers opinions though :)

Yeah, if this was a opportunity for me in real life with my actual circumstances rather than the ones listed by the OP, I'd Kelly it (or something close to what Kelly calcs would give). My post above was serious though.


A few points:

You use Kelly to maximize the geometric mean of outcomes. That's great in the long term, but if I have fairly mediocre prospects over a two year period after which I retire, I'd rather over stake and increase the probability of an (exceptionally) favourable result.

Pure Kelly works under a very limited set of conditions. For almost any real life scenario there are more variables to consider, so Kelly isn't optimal. Adapting Kelly to trading on Betfair is very complex, due to the changing nature of the the exchange. If you programmed a bot to trade on Betfair, working out not just the edge on each bet, but likelihood of getting matched when offering, likelihood of being able to trade out to reduce risk, impact of increase in stake size on profitability, and other useful variables, you would do better than Kelly by properly factoring them in. You will never be able to derive an equation on such a fundamental level as Kelly, it would need to be changed frequently based on what other people are doing.

If you use full Kelly in this scenario and lose £61k you're in a position where you will make more from the job than from gambling (assuming the edge doesn't increase with a smaller capital base).

It's almost certain that a £61k loss will introduce a non-negligible risk of ruin if sticking with gambling that simply applying Kelly does not show. This is due to having £49k left with no savings, forcing £2k a month withdrawals for living expenses. It's possible that winnings will not cover this, slowly bringing the account closer to zero.



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Here's an example of thinking beyond Kelly that I've given before on the forum in some form or other:

You have an income of £10k net a month adjusted for inflation for life and £2k a month living expenses. You currently have a net worth of £100k all in cash. You are given the betting opportunity as described by the OP as a one off. How much of your net worth do you risk?

I just wonder how people describe these answers, I'm studying Finance and any true gamble is ill advised unless you do bet so where are all the answers coming from? pros?

erm...

what does this mean? "any true gamble is ill advised unless you do bet"

and who is the 1 female?