backing by kelly plan question

[mcbee]

hi
i am trying to get my head around this plan but when i look at the formula in the trigger it is different than the formula in tsm.
trigger formula from the trigger example
The formula for the Expectation will be the opposite:

Expectation = StrikeRate * Stake * (AverageOdds - 1) - (1 - StrikeRate) * (Stake - (Stake * Commission))

the actual trigger formula for the Expectation is.
(s_rate/100)*(avg_odds-1) - (1 - s_rate/100)*(1-commission)
the actual betting trigger formula is.
(((expectation * (back_price - 1))/divisor)*base)/(back_price-1)

TSM formula
((odds x estimation) - 1) / (odds - 1) = (result) x 100 (this is the bank amount)

if i use the trigger it bets the same amount.
i have made a formula to   (back_price*(26/100)-1)/((back_price-1)*(bet_base/7)) without the kelly triggers.
and it alters the bet amount to suit the odds, the 26/100 is my strike rate, bet_base is my bank and the 7 is my divisor.
but why doesn't the kelly trigger work.


mcbee

[stillout]

What do you mean "kelly trigger doesnt work"? I have used this staking plan for several testings and it worked for me the way it suppose to. Its a good plan but only on markets with big volume of money because in other cases the prices of the market may not respond to reality and lead Kelly to false estimations

[mcbee]

hi
have you used the backing kelly or laying kelly.
with the backing the bet amounts are the same, apart from lowering as the bank lowers.


mcbee

[stillout]

yes and for what i can remember it was working fine. Did you set average odds variable correctly? I attach my last test-trigger with backing by kelly plan

[mcbee]

hi
thanks for the help, but NO the trigger does not work as it should.
i have found an error in the back trigger formula, so i will send an email to support.


mcbee

[stillout]

thats good to know because i am planning to use  this stake plan in the near future

thanks

[Oxa (WellDoneSoft)]

I am looking into this, will take some time to test it.
I will let you know the results as soon as I have them.

Update.

I've looked once more into the original Kelly criterion.

Mcbee is right: if you take the formula (b*p - q)/b, then replace q with (1 - p), and take into account that b is (B - 1), where B is the digital price of a horse, then you can make the following transformations:

(b*p - q)/b = (b*p - 1 + p)/b = (p*(b+1) - 1)/b

B = b+1

(p*(b+1) - 1)/b = (p*B - 1)/(B - 1)

whereas in the trigger example we had (p*(B - 1))/(B - 1), which is indeed devoid of sense, because in that case you could just cancel (B - 1).

Very well done Mcbee!

I have corrected the trigger example and the file to which it links.
Many apologies for the error.

Please mind that either the expectation or back odds should be high enough for a bet to qualify.

[mcbee]

hi oxa
thank you for the alteration so quickly.


mcbee

[mcbee]

hi oxa
a question, is the kelly staking plan based on chances to win.


mcbee

[Oxa (WellDoneSoft)]

a question, is the kelly staking plan based on chances to win.

It is based on your expectation, which is close to chances, but is customizeable, i.e. not absolutely objective.

In that particular example, which in its turn is based on the TSM algorithm, the expectation is based on the previous history of winnings and on the average price of the selection that you back / lay. So it is a combination of the winning rate and digital odds of winning which are offered by other bettors.

Or am I misinterpreting your question?

[mcbee]

hi
the answer is what i expected, thank you.
now for the follow up, if the winning chances are greater then you would bet more money on that, but if the winning chances are poor then you would bet less money.
am i correct.
if so we have another problem.


mcbee

[bamthwok]

Hi,

I did not check on the formulas but I'm not sure whether one major element of the Kelly Staking Plan has been understood correctly.

As with all staking plans, Kelly only does make a sense if your trigger is profitable with level stakes.

With Kelly you have to estimate the real odds of winning.

As this is difficult the only reliable method you have is to base your estimation on your betting history. Of course it requires a  sufficiently large database. If in profit, the estimated odds for the future will be based on your P/L history.

For example average Betfair odds for your last 100 bets are 2.0 but you have won 60 of your last 100 bets then your estimated odds would be 100/60=1.66667.

Your stake will be calculated as follows:

 Stake = ((Odds *Perc) - 1) / (Odds - 1) * 100

In our example:

Stake = ((2.0*0.6) - 1) / (2 - 1) * 100 = 20%

So your stake is 20% of your betting bank.


This is my understanding of Kelly. Are you guys thinking the same way? Does the calculation in the trigger works like that?

Cheers,
bamthwok

[mcbee]

hi
so, should the stakes get bigger as the greater chance of winning and get less as the less chance of winning.


mcbee

[bamthwok]

Not really. It depends on your odds advantage (odds estimation).

Example:

Assuming your bank is 1000


Scenario 1:

Average Betfair Odds  4.0 (25% chance of winning)

Real winning percentage 28% (factor0.28, real odds: 100/28 = 3.57)
(as per betting history)

Stake = ((4*0.28)-1) / (4-1)  = 1.12-1 / 3  = 0.04  = 4%

Stake = 1000 *4% = 40


Scenario 2

Average Betfair Odds 3.0 (33.33 chance of winning, higher than before)

Real winning percentage 35% (factor 0.35, real odds 100/35 = 2.86)

Stake = ((3*0.35)-1) / (3-1) = 0.05 / 2 = 0.025 = 2.5%

Stake = 1000 *2.5% = 25


As we can see, although the chance of winning in scenario 2 is higher, the actual betting amount is less. This is because your edge over the betfair odds is higher in scenario 1.

So your stake will not be calculated new for every bet, it's a fixed percentage of your betting bank (you can calculate your betting bank after every bet or, easier, manually after every day of betting).

This percentage is (most likely) based on historical betting data (average betfair odds and real winning percentage) unless you are able to compile your own odds for every single event.

Again this is my understanding of Kelly. Not sure whether there are different interpretations.

Cheers,
bamthwok

[mcbee]

hi
one more question, where does the first 4 come from in the Scenario 1:

Stake = ((4*0.28)-1) / (4-1)  = 1.12-1 / 3  = 0.04  = 4%

and thank you, if your answer is what i think it is, then i have found somebody that understands the plan.
then i will continue, with your help.

mcbee