Our
Forum has Moved - Please CLICK
HERE to go there now.
This forum will remain open as an archive only and cannot be posted
in but can be read.
Please go to the New
forum and Register as a Member!
The work I am posting today does not bring (to most of you) too many new facts, I guess. It is, however, the result of some (many, in fact) days of hard work developing, testing and running a model in order to determine some betting criteria. These criteria, at first, were intended to guide my own betting policy but, as the work progressed, I could not resist the temptation to share this data with you. I hope some of you may become interested and take some advantage from this posting.
I decided to build up a numerical model to simulate and determine the risk of losing all the money (and have an idea on some other points as you will see below) when following a fixed stake policy. I have to confess, however, that my secret desire was (is!?) to find a mathematical reason to support a progressive staking strategy (to no success up to now, however).
Basis of the work were:
Flat stakes during the simulation, meaning that the number of units staked per bet are kept constant for each simulation;
Each simulation consisted of 10,000 runs of a set of 2,000 bets each run (Why 2,000? Because I assumed a serious punter should be on ca. 5-7 bets per day, as an average, making up app. 2,000 bets a year);
Simulations were done considering two variables:
stake size (1%,2%,3%,4%,5%,7%,10%,15% and 20% of the initial bank and kept constant unitwise for the simulation);
strike rate (50% thru 60% with a 1% interval) in order to check how findings vary with the punter ability to predict correct results;
Note: I used a constant odd of 1.90. I used this because this is an odd that can be achieved in almost any football match (asian handicap), or basketball, american football (spread betting),etc. Please note that the model can also use different odds (say e.g. 30% of 1.50, 40% of 1.70 and 30% of 1.90 odds) if we deem necessary. Results and conclusions being presented today, however, are applicable for 1.90 odds.
Calculated outcomes of the model for each simulation (set of 10,000 runs of 2,000 bets each run) are:
Probability of losing all the money sometime during the 2,000 bets (season);
Percentage of time when the punter current bank is lower than the maximum bank already achieved in the past bets ( this is an wonderful insight to give us some soul comfort when we realize that on one given day, our bank is, say, 88% of the maximum bank we had achieved in the past, during the same season). For your information, I can guarantee that most of the punters should be below the maximum achieved bank more than 95% of the time (most likely even more than 95%);
Average estimated final bank (when not losing all the money);
Average estimated maximum bank (sometime during the 2,000 bets) also when not losing all the money.
Main findings are:
For the losing all the bank probability please check the below table;
Average final bank figure, does not significantly (as expected) differ from the hand-calculator easily calculated ones;
Small details (such a 1% higher strike rate) make a lot of difference. Therefore, it pays off to devote some (much?) time and effort to gather info, data, etc. on betting events. Each 0.1% you can increase in your strike rate is worth of it.
Now, take a look at the table below and tell where you are (or should be).
I will be back with more on this subject soon.
Abraços.
This message has been edited by Jhim on Mar 5, 2003 6:03 PM
I trust that you have also discovered from your simulations that where the punter doesn't have a winning edge, there is no staking plan on Earth that can turn losses into profits over the long term, no matter how much you try. This is really the fallacy of progressive staking plans.
Jhim: thanks for the support and I hope next time I can get everything done. Problem is that I am away from my country with a very old PC. When I get hoem, hopefully next Saturday, I'll check all your hints in order to determine where I failed.
Joe: of course I read your comments. Problem is that I was too busy to get the table posted that I could not reply. By the way, how the figures I got compare to yours?
Joe, I know that any progressive staking plan is a complete madness. I kind of joked in my post. for the record, I always considered your postings as the best wherever I saw them.
Re: Are you in the way to lose your bank ? (2nd try)
March 6 2003, 10:54 AM
Hi zoccer, thanks for the compliment
It's hard to comapre my results for level staking to yours because firstly you've chosen 2,000 bets (I chose 250 which I think is closer the most punters annual bet turnover) and secondly because you've set the analysis parameters slighly different to mine. You've fixed the odds and varied the strike rate (thus in effect varying the punter's edge). I've varied both the punter's average edge and the average odds, and for each edge-odds scenario, I varied the edge and odds throughout the 250 bets series to try and make things more realistic.
Anyway, in broad terms your percentage values for bankruptcy look very similar to mine in the sense that without the winning edge, things can go pear-shaped much more easily, but even with the winning edge, one should avoid staking too high. 5% of starting bankroll for level staking is what I would consider the absolute top limit (personally I'd be no higher than 3%) and I think your figures support that.
Yes, from what I remember seeing in your posts our figures seem to be in the same range. I am now preparing myself for a new stage of the study.
However, I have not made up my mind on what is the most interesting next step:
1) keep the 1.90 odds and try to vary the stakes (keep it the same % in some ranges, e.g.: 1 unit for a bank 100-125; 1.25 units for a bank 125-150; 1.50 units for a bank 150-175; etc..
or
2) keep the same staking scheme and adopt a new odds distribution, e.g. 40% 1.50 + 30% 1.70 + 30 % 2.00
Re: Are you in the way to lose your bank ? (2nd try)
March 6 2003, 3:23 PM
Depending on your time and processing power you could do both.
Instead of testing a plateau staking plan, i.e increase stake size after bankroll reaches certain size, why not investigate % bank staking, where the stake size is 1%, 2%, 3% etc. of the bankroll at the time the bet is made. Obviously in the real world when placing more than one bet at a time this isn't possible, but you get a feel for what % bank staking is inherently capable of returning.
With my simulations I also investigatd the probabilities of the bank being in profit at the end of the betting series.
If you investigate % bank staking who will find that the chances of losing your bankroll are virtually none for any winning system and very small even for losing ones (theoretically zero but in the real world you have to set a limit size after which you count the bank as lost - I took 1% of the starting bankroll). If you compare the size of finishing banks, % bank staking can be much more profitable (as you'd expect) for winning systems. However, when you compare the chances of actually being in profit after x number of bets with level staking, it is actually lower (when comparing like for like). This is because if you lose early on, it takes longer to recover back to your starting bankroll. This may appear an elementary point but when it comes to betting in real time the influence this lower probaility will have on a punter's betting psychology is not insignificant.
As a summary, with % bank staking, when you profit, you tend to profit more, but less often (in terms of time increments) than for level staking.
If you test your proposed plateau staking plan (something I didn't do) I'd imagine the results will lie somewhere in between those for level staking and % bank staking.
Varying the odds is worth analysising too. Do this for level stakes and you will see that the risk of losing your bankroll is much higher for longer odds (because of the effects of longer losing runs). The punter's solution to this is to reduce stakes on longer odds, in effect adopt a fixed profits staking plan. This plan is actually as profitable as level staking but somewhat safer.
You might even want to look at Kelly staking (a mix of fixed profits and % bank staking). A Kelly stake is calcuated by using the betting edge, meaning that the punter has to have some awareness of what it is, meaning he will need to do some sort of odds and value analysis. A Kelly stake size is simply (edge-1)/(odds-1). If for example bookies odds were 2.2, but you believe the result to have a 50% chance of occurring (fair odds 2) then your perceived edge is 1.1, and your Kelly stake is then (1.1-1)/(2.2-1) = 0.0833 or 8.33% of your bankroll. Clearly, Kelly staking can lead to highish advised stake sizes and for this to work well, you need to be confident and accurate in you assessment of betting edge. Conservative Kelly stakers might half or even quarter their advised Kelly stake size. Theoretically, Kelly staking offers a maximisation of bankroll growth for a minimisation bankruptcy risk. In practice it can be quite bad news for those who don't know what they are doing.
I'd be strongly in favor of fixed stakes for long periods of times. You contemplate increasing stakes as your bank grows (one size of stake for 100-125% bank, another for 125-150% bank etc), but what will you do if your bank shows a loss?
I'd say keep your stakes fixed - in experiments and in real life situations.
Current Topic - Are you in the way to lose your bank ? (2nd try)
