Optimal stake

GoldenBoot

What is the best staking strategy to maximise profits in the scenario below other factors aside.

50 football bets placed over the season at odds of 1.57 each.

There will be 40 winners and 10 losers.

Thanks.

GoldenBoot

Also can you specify if your staking strategy uses current or starting bank strategy and why.

thanks.

Soldie

I like to go with level staking, with 1 unit representing 1% of my bankroll. In some cases I'll increase my bet size to 2% or 3% if I'm more certain of the results, and in extremely rare cases 5%. More progressive staking strategies are tantamount to chasing your losses, and I don't like to do that.

GoldenBoot

Its crucial to get the staking right if you are able to calculate your edge to maximise value. 1% would be far too low in this scenario.

clived2

1.57 odds
You proclaim 1 in 5 bets will lose 1.2 odds

I dont see how you are going to gain an edge of 1.2 to a bookies 1.57
You are proclaiming some serious knowledge here, Anyways that is neither here nor there.

You should not bankroll for your perceived value ie 1.2 your bankroll should be set up for statistcal variance of 1.57 over 50 bets and then your percieved value 1.2;) would be profit,

I could work it out but I am at work at the moment,:pac:

GoldenBoot

I have put in a lot of time and experience intrepreting match stats to be able to make this claim over just 50 bets a season. This is the last detail.

if you have time after work i would appreciate a write up.

ft9

I hope your gonna share your work with us?

clived2

GoldenBoot wrote: »

I have put in a lot of time and experience intrepreting match stats to be able to make this claim over just 50 bets a season. This is the last detail.

The reason you require an optium stake amount is not to lose your bankroll
over certain statistical anomalys. Are you suggesting using 1.25 with just a group size of 50 bets (very low group size)

GoldenBoot

There are not many betting opportunities which give an expected roi this high so it would have to be over a sample size of just 50 selections. I know this will greatly increase the variance each season. If you could also give an insight into the risk of ruin that would be a great help.

clived2

I will do something when I go home, a few questions,

Are you betting with your new bank each time or a % of starting bank

You say you have done research, can you provide your winning streak, ie most selections in a row that won and most that lost in a row, this is required for standard deviation.

Your odds 1.57 and your expected true value 1.25 for 50 bets are very extreme to say the least. I not saying this isnt true but say for example Kellys Criterion( a well known and relatively sucessfull staking plan) uses
Actual Value versus your expected value 1.57-1.25= .32 diveded by 1.25 25.6% value:eek: divided by 1.57-1= wait for it......... 44.9 per cent of your bank,
2 losses in a row and you are ruined as you would put it.

Now say for example your expected value was 1.4= 20% of your bank.


The Kelly Criterion has been applied with more caution and alternate formulaes exist to avoid losing ones bank depending on which of the following you want to be.
High Risk.
Medium Risk.
Low risk.

I could calculate a staking plan wherby the probalbility of bankruptcy is 10 to 1, 100 to 1, 1000 to 1, 1 million to 1 however your bet range is only 50 bets too small a range for any kind of accuracy also all this will go out the window if you provide inaccurate data, ie expected return odds:)
One must note proving to be risk adverse, will result in stakes of 1% of bank which would be a waste of time considering small set size 50

GoldenBoot

Thanks clive.

I'm currently betting new bank each time using a half kelly strategy.

8 wins in a row and 2 loses in a row.

clived2

GoldenBoot wrote: »

Thanks clive.

I'm currently betting new bank each time using a half kelly strategy.

8 wins in a row and 2 loses in a row.

So you are using half kelly stategy, what do you need me for;)

GoldenBoot

From what i have read i understand assuming edge to be accurate that a half kelly results in a 10/1 odds of halving bank before doubling it. I want to be able to work this out for myself so i can tailor individual staking plans to a persons own appetite for risk versus reward. An offshoot of this is that i can incorporate this into my interest in finance.

thedini

Using a sample size of 50 and a strike rate of 80% the longest losing run that you would be expected to encounter is 2.43. There's no way I would be betting 41.15% of the bank on each bet. I'd be using max 10% so as to be more risk-adverse.

RefulgentGnomon

clived2 wrote: »

I will do something when I go home, a few questions,

Are you betting with your new bank each time or a % of starting bank

You say you have done research, can you provide your winning streak, ie most selections in a row that won and most that lost in a row, this is required for standard deviation.

Your odds 1.57 and your expected true value 1.25 for 50 bets are very extreme to say the least. I not saying this isnt true but say for example Kellys Criterion( a well known and relatively sucessfull staking plan) uses
Actual Value versus your expected value 1.57-1.25= .32 diveded by 1.25 25.6% value:eek: divided by 1.57-1= wait for it......... 44.9 per cent of your bank,
2 losses in a row and you are ruined as you would put it.

Now say for example your expected value was 1.4= 20% of your bank.


The Kelly Criterion has been applied with more caution and alternate formulaes exist to avoid losing ones bank depending on which of the following you want to be.
High Risk.
Medium Risk.
Low risk.

I could calculate a staking plan wherby the probalbility of bankruptcy is 10 to 1, 100 to 1, 1000 to 1, 1 million to 1 however your bet range is only 50 bets too small a range for any kind of accuracy also all this will go out the window if you provide inaccurate data, ie expected return odds:)
One must note proving to be risk adverse, will result in stakes of 1% of bank which would be a waste of time considering small set size 50

More like (1/1.25) - (1/1.57) = 80% - 64% = 16% of your bank

clived2

RefulgentGnomon wrote: »

More like (1/1.25) - (1/1.57) = 80% - 64% = 16% of your bank

I dont know what you are talking about, this is the kelly criterion


http://en.wikipedia.org/wiki/Kelly_criterion

GoldenBoot

RefulgentGnomon wrote: »

More like (1/1.25) - (1/1.57) = 80% - 64% = 16% of your bank

Can you explain the benefits of this over the kelly criterion or other staking plans?

---

Can anybody explain the math behind the kelly criterion having the following charastics?

full kelly: 3/1 to half bank before doubling it.
half kelly: 10/1 to half bank before doubling it.

Mellor

clived2 wrote: »

Actual Value versus your expected value 1.57-1.25= .32 diveded by 1.25 25.6% value:eek: divided by 1.57-1= wait for it......... 44.9 per cent of your bank,
2 losses in a row and you are ruined as you would put it.

I use this format, but its the same result eitherway



But it works with fractional odds, not decimal.
So for the case in the OP

[(.56)(.8)-(.2)]/.56

Do you have your method in a generic form?

GoldenBoot wrote: »

Can you explain the benefits of this over the kelly criterion or other staking plans?

He was trying to do Kelly, he got it wrong.

Can anybody explain the math behind the kelly criterion having the following charastics?

full kelly: 3/1 to half bank before doubling it.
half kelly: 10/1 to half bank before doubling it.

I'm not sure what you are asking here.

For half kelly, you work out the kelly% and half it against your full roll, or apply it it full to half your bankroll (both are the same, which ever your prefer to use)



KC is great in theory, but the problem is that we cannot say with high accuracy the odds of an event occuring, we have to estimate it. Half or 3/4 kelly allows for this were we are off to protect us. Underbetting (which is far better than over betting) like this reduces our expected utility, but also reduces our risk of ruin.

Taking it for a range of matches like you did in the OP is wrong.
I have no idea where you go those figures.

But say its for a certain football team. They on average with 40/50 games a season, and average odds are 1.57 (just copying your figures, this situation doesn't exist imo)
Their chances of winning, as well as their odds change from match to match, so would the optimal stake. They might not even be +EV every match, where KC says not to bet.

The numbers you quote are a huge edge, one so big that I honestly doubt that it exists, certainly not over a long term situation. Your research is wrong, you've over estimated, getting this info right is far more important than getting max value via Kelly's Criteron.

If you do insist it exists*, then don't worry about optimal bets, just punt it all the time as its +EV.

*Also, prove it

GoldenBoot

Its the 2.5 goal market. The edge is there but only for approx 50 games per season in the 5 main european leagues so its important i maximise value. I will post a log im keeping at the punters lounge at the end of the season.

I will stick with the half kelly for the remainder of this season.

Mellor

but how do you know that odds are going to average at, or be at 1.57 for those 50 matches?

GoldenBoot

Quote:
Can anybody explain the math behind the kelly criterion having the following charastics?

full kelly: 3/1 to half bank before doubling it.
half kelly: 10/1 to half bank before doubling it.
I'm not sure what you are asking here.

-->For half kelly, you work out the kelly% and half it against your full roll, or apply it it full to half your bankroll (both are the same, which ever your prefer to use)

-->The percentage selected by kelly are the optimal growth rates and the above stats are the odds of halving your bankroll at any stage during the run according to the calculator I use here.

Mellor wrote: »

but how do you know that odds are going to average at, or be at 1.57 for those 50 matches?

The odds are relatively low for the games i select. 1.57 to 1.67 in more than half the matches. When looking to stake, as you say its better to underbet than over bet. The average will be slightly over 1.6.

Thanks for the help lads.

hsanz114clayton

WT.........................F

Impressive guys!I wish I could understand.Can you explain what you are doing in leymans terms please?
Much appreciated

GoldenBoot

Read the wikipedia page for kelly criteron.
basically we are discussing risk versus reward to our bankroll in order to strike a balance we are comfortable with once we have identified a profitable bet. Beyond that you will need to figure out google and get reading. Its fairly crucial if you want to make money gambling. It also requires work and patience that 98% of people on betfair seemingly lack.