This exchange of messages, which you will read below, took place between me and one Mr Aswin Patel (USA) two days ago on Mr Rajgopal Nair’s blog. Mr Patel had earlier written that a bookmaker once offered to pay him Rs 5 lakh for Rs 10,000 if he could nominate 10 half-money horses IN_A-ROW (win or place did not matter), or Rs 1 crore for Rs 10,000 if he could nominate 10 even-money horses, again, IN-A-ROW.
When Mr Aswin Patel visited my blog on Saturday and saw that there were 11 successful place bets IN-A-ROW, he wrote to me:
Mr Gosavi,
I noticed that you were successful in giving 11 winners in place, in a stretch, I do not know if they were strictly place bets or e/w bets and do not know if the Payouts were more than 1/2 money or Rs 15 for place which is one factor necessary to be correct.
If they were place bets KUDOS to you.
Aswin Patel
My reply was:
Dear Mr Ashwin Patel,
My all 19 bets over the last 13 race days were tipped as WIN bets, but since this is a public trial, I am also keeping track of the PLACE dividends.
Since you have asked this question, just for academic interest, if one had put a Rs10,000 roll on the last 11 successful PLACE bets, as per the BTC dividends, he would have got a profit of Rs 4,84,160 which is very close to the Rs 5 lakh figure that you talked about to begin with. And as you know, having consecutive successes has much more to do with luck than to any handicapping skill. Just plain lucky is how I feel when I look at those 11 consecutive successes.
Prakash Gosavi
As I went to bed that night, I wondered if I was really ‘lucky’ as I wrote to Mr Patel, or whether 10 successful place bets IN-A-ROW should be considered ‘normal’ for the FINOO (Follow-In-Next-Outing-Only) method.
Suddenly, I remembered my old research notebooks. These are four 200-page, ledger-size notebooks which I used between 1990 & 1998 when I was in brilliant (pardon the self-praise) mathematical form, and invented formulas (I was then known by my pen name Speculus) for predicting the ‘Number of strides’, developed mathematical framework for ‘stride angle and its connection with form’, the effect of turn on speed of horses, and also the formula for accurate timing up to 1/100th of a second which, incidentally, is now used the world over by hundreds of pace handicappers as a useful tool. During the same period (with nothing better to do in spare time except getting frustrated at the fact that all this wonderful research was only turning out to be academic and was not exactly adding to my bottom line), I had also toyed with devising a formula to predict the biggest winning streak or losing run for a horse race player who knew his average strike rate over the long run. Was it still there in those pages? I would check first thing the next morning, I thought and went to sleep.
That formula was a personal milestone for me in my research about money management, a subject I first learnt from one of the finest souls--Dick Mitchell.
Late Dick Mitchell, noted American handicapper/writer who introduced me to the subject of money management, had suggested using the random number function (now easily available on even scientific calculators) to simulate a series of wins and losses to predict the longest losing streak for a gambler. The random number function generates a random number between 0 & 1 (say .38 or .07 or .86) every time you hit the key.
Dick’s concept was quite scientific, but extremely tedious.
He proposed that if you were, say, a 35% handicapper (that means your long term historic record shows that, on the average, you win 35 of the 100 races you bet), then there is a way to manage your money so that your worst losing run does not take you beyond your comfort zone. All you have to do is generate a series of 100 (or 500 or 1000, whatever you think as number of bets you would make over the long term—it may be six months or a year or 3 years, or whatever) random numbers by using the random number function (denoted generally as Ran# on most calculators), and catalogue all the results. Then treat any figure that is .35 or less as your WIN situation and all others (greater than .35) as your LOSS situations, and re-write the whole matrix with W or L replacing the figures. Now, count the maximum number of L’s that are in sequence, that’s your longest losing run in that sample. Then repeat the whole process for another series and again record the maximum number of consecutive L’s. After doing this process a number of times, you can arrive at a reasonable ‘average’ value of L (your possible maximum number of losses IN-A-ROW). Once you arrived at this number, then the rest of the process was fairly simple.
If you define your comfort zone as NOT losing more than two-thirds (66%) of your betting capital, and for your 35% strike rate if you got the figure of L=11 (meaning you expected to lose maximum 11 bets in a row in worst-case scenario), then just divide 66% by 11 and the answer, 6%, tells you that you should NEVER bet more than 6% of your capital on ANY bet if you wish to always stay within your comfort zone.
Dick’s logic was superb, his method scientific, but it was extremely tedious and boring. How nice it would be if you could just put your winning (or losing) percentage in a formula, and it would give you your longest losing run (or longest winning streak), I thought.
Fortunately, I came across a website on probability by Peter Webb, a self-proclaimed speculator/investor himself. He had listed an approximate, but excellent, formula for the longest winning/losing run on the site. However, a check revealed that the formula broke down for higher strike rate and lower number of trials (bets), giving absurd answers like 14 straight wins from 10 bets (for the strike rate of 85%), so I had to start thinking afresh.
By the grace of God, I was soon able to introduce a correction to Peter Webb’s formula (to strive for the accurate formula was beyond my math training as well as intellectual ability, I must admit) that would give a near-accurate answer to the desired question of the longest winning streak or losing run.
Was that formula still sitting somewhere in my old notebooks? I wondered.
The first thing I did on Sunday morning was to take out the notebooks and scan them. And sure enough, there it was, this useful little mathematical tool staring at me from one of the pages. To make understanding simpler, just put this formula in an excel sheet and let it work out the answer for you:
Where T is the number of trials (or in our case, BETS to be made),
N = longest winning streak or losing run
P = percentage (win or loss) expressed as a probability between 0 & 1
while ROUND and EXP are MicroSoft Excel functions.
You can try it yourself by inputting excel cell addresses in place of T, N & P values to generate answer to your queries about what can be your longest winning streak or losing run at the current level of handicapping skill, and base your decisions, especially related to management of betting capital, on it.
Now, let me come back to the problem I started with. Was it really a matter of luck (as I wrote to Aswin Patel) to have 11 successes in a row? Or should it be considered “normal” for a system that was expected to give 80+% results for place?
Here is the table generated by the formula that lists, for various success %, the number of bets to be made to have 11 straight successes in a row. Have a look at it:
The table tells you at a glance that for a method with 80% strike rate one needs only 22 bets to have a winning run of 11 successes in a row. So when the current percentage is even better than 80%, it is no surprise FINOO has had 11 successes in a row in just 19 bets. It is not a matter of luck at all, it is a simple matter of the law of probability.
Do make a note of the 50% strike rate case (which, in racing, is considered quite a decent %) which says that 11 straight successes will come only ONCE in 2,058 bets!
Assuming Mr Nair tips 2 to 3 bets a day for the remaining 18 days of the season, that’s about 40 to 50 bets until the end of season before which he must accomplish the task. The table shows that he can expect to do it in 44 bets provided he strikes a success rate close to 70%.
He will need to hit exceptional form to have that kind of rate especially for the WIN category. But it’s not impossible. Let’s hope and pray he does it. The whole secret and winning strategy required for his success is given by the formula as displayed by the figures in the highlighted row: He must strike, maintain and sustain a success rate of 70%, and he must tip at least 44 bets to realistically hope to achieve the target of 10-in-a-row. If he can do it, then it will not be a matter of luck at all—it will be purely a matter probability (and of course his handicapping skill which is reflected in the figure of 70%).
But suppose he accomplishes 10 straight winning bets with only 50% strike rate and only 30 bets (this means 15 successes, 10 of which must be in a row) then, although the feat in itself will be an extraordinary case of brilliant handicapping skill, having 10 of the 15 winners IN A ROW will have to be treated as a matter of exceptional luck.
After all, luck also has its own mathematics, and not much different from the laws of probability, as the formula above explains.
Dick’s concept was quite scientific, but extremely tedious.
He proposed that if you were, say, a 35% handicapper (that means your long term historic record shows that, on the average, you win 35 of the 100 races you bet), then there is a way to manage your money so that your worst losing run does not take you beyond your comfort zone. All you have to do is generate a series of 100 (or 500 or 1000, whatever you think as number of bets you would make over the long term—it may be six months or a year or 3 years, or whatever) random numbers by using the random number function (denoted generally as Ran# on most calculators), and catalogue all the results. Then treat any figure that is .35 or less as your WIN situation and all others (greater than .35) as your LOSS situations, and re-write the whole matrix with W or L replacing the figures. Now, count the maximum number of L’s that are in sequence, that’s your longest losing run in that sample. Then repeat the whole process for another series and again record the maximum number of consecutive L’s. After doing this process a number of times, you can arrive at a reasonable ‘average’ value of L (your possible maximum number of losses IN-A-ROW). Once you arrived at this number, then the rest of the process was fairly simple.
If you define your comfort zone as NOT losing more than two-thirds (66%) of your betting capital, and for your 35% strike rate if you got the figure of L=11 (meaning you expected to lose maximum 11 bets in a row in worst-case scenario), then just divide 66% by 11 and the answer, 6%, tells you that you should NEVER bet more than 6% of your capital on ANY bet if you wish to always stay within your comfort zone.
Dick’s logic was superb, his method scientific, but it was extremely tedious and boring. How nice it would be if you could just put your winning (or losing) percentage in a formula, and it would give you your longest losing run (or longest winning streak), I thought.
Fortunately, I came across a website on probability by Peter Webb, a self-proclaimed speculator/investor himself. He had listed an approximate, but excellent, formula for the longest winning/losing run on the site. However, a check revealed that the formula broke down for higher strike rate and lower number of trials (bets), giving absurd answers like 14 straight wins from 10 bets (for the strike rate of 85%), so I had to start thinking afresh.
By the grace of God, I was soon able to introduce a correction to Peter Webb’s formula (to strive for the accurate formula was beyond my math training as well as intellectual ability, I must admit) that would give a near-accurate answer to the desired question of the longest winning streak or losing run.
Was that formula still sitting somewhere in my old notebooks? I wondered.
The first thing I did on Sunday morning was to take out the notebooks and scan them. And sure enough, there it was, this useful little mathematical tool staring at me from one of the pages. To make understanding simpler, just put this formula in an excel sheet and let it work out the answer for you:
T = ROUND(EXP((N*(-LN(P)))),0)+(N-1)
Where T is the number of trials (or in our case, BETS to be made),
N = longest winning streak or losing run
P = percentage (win or loss) expressed as a probability between 0 & 1
while ROUND and EXP are MicroSoft Excel functions.
You can try it yourself by inputting excel cell addresses in place of T, N & P values to generate answer to your queries about what can be your longest winning streak or losing run at the current level of handicapping skill, and base your decisions, especially related to management of betting capital, on it.
Now, let me come back to the problem I started with. Was it really a matter of luck (as I wrote to Aswin Patel) to have 11 successes in a row? Or should it be considered “normal” for a system that was expected to give 80+% results for place?
Here is the table generated by the formula that lists, for various success %, the number of bets to be made to have 11 straight successes in a row. Have a look at it:
The table tells you at a glance that for a method with 80% strike rate one needs only 22 bets to have a winning run of 11 successes in a row. So when the current percentage is even better than 80%, it is no surprise FINOO has had 11 successes in a row in just 19 bets. It is not a matter of luck at all, it is a simple matter of the law of probability.
Do make a note of the 50% strike rate case (which, in racing, is considered quite a decent %) which says that 11 straight successes will come only ONCE in 2,058 bets!
Don’t believe it? Get a friend for company and start flipping a coin (probability of heads or tails is both 50%) and record how many times you get either 11 straight heads or tails in 2,058 tosses. I am sure you will get convinced.
Another interesting thing. Look at the .35 figure in the table which is generally the public’s win percentage. For the public choices or favourites to win 11 races in a row you need over a hundred thousand races to be run. It means that if you see that happening more often than the laws of probability demand, be sure the races are heavily rigged in favour of the fancied horses, or most of the horses in most of the races are simply non-jobbers, thus tilting the balance in favour of fancied horses whose strike rate is defying the mathematical probability.
When you see straight 21 races at Ooty racecourse being won by the first favourites (I did, in 2003), you know a highly improbable event has become reality because of some extraneous forces and their machinations.
The point I want to make is in horse racing exceptional success or exceptional failure must always be viewed in terms of the strike rate and strike rate alone. FINOO’s stupendous success in PLACE is in keeping with its present strike rate, as is clear by the formula given above.
Post script: Mr Rajgopal Nair, famous on the web with his pen name Destiny Calling, on whose blog I exchanged messages with Mr Aswin Patel, has announced on his blog that he would try to tip 10 successful bets in both the WIN and PLACE categories BEFORE the end of this Bangalore summer season 2009!
How probable is that?
Let us run the formula and generate a table for 10 straight successes like we did for 11. Here is how it looks:
Another interesting thing. Look at the .35 figure in the table which is generally the public’s win percentage. For the public choices or favourites to win 11 races in a row you need over a hundred thousand races to be run. It means that if you see that happening more often than the laws of probability demand, be sure the races are heavily rigged in favour of the fancied horses, or most of the horses in most of the races are simply non-jobbers, thus tilting the balance in favour of fancied horses whose strike rate is defying the mathematical probability.
When you see straight 21 races at Ooty racecourse being won by the first favourites (I did, in 2003), you know a highly improbable event has become reality because of some extraneous forces and their machinations.
The point I want to make is in horse racing exceptional success or exceptional failure must always be viewed in terms of the strike rate and strike rate alone. FINOO’s stupendous success in PLACE is in keeping with its present strike rate, as is clear by the formula given above.
Post script: Mr Rajgopal Nair, famous on the web with his pen name Destiny Calling, on whose blog I exchanged messages with Mr Aswin Patel, has announced on his blog that he would try to tip 10 successful bets in both the WIN and PLACE categories BEFORE the end of this Bangalore summer season 2009!
How probable is that?
Let us run the formula and generate a table for 10 straight successes like we did for 11. Here is how it looks:
Assuming Mr Nair tips 2 to 3 bets a day for the remaining 18 days of the season, that’s about 40 to 50 bets until the end of season before which he must accomplish the task. The table shows that he can expect to do it in 44 bets provided he strikes a success rate close to 70%.
He will need to hit exceptional form to have that kind of rate especially for the WIN category. But it’s not impossible. Let’s hope and pray he does it. The whole secret and winning strategy required for his success is given by the formula as displayed by the figures in the highlighted row: He must strike, maintain and sustain a success rate of 70%, and he must tip at least 44 bets to realistically hope to achieve the target of 10-in-a-row. If he can do it, then it will not be a matter of luck at all—it will be purely a matter probability (and of course his handicapping skill which is reflected in the figure of 70%).
But suppose he accomplishes 10 straight winning bets with only 50% strike rate and only 30 bets (this means 15 successes, 10 of which must be in a row) then, although the feat in itself will be an extraordinary case of brilliant handicapping skill, having 10 of the 15 winners IN A ROW will have to be treated as a matter of exceptional luck.
After all, luck also has its own mathematics, and not much different from the laws of probability, as the formula above explains.
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This has reference to Prasad's query (in the comments section) about my money management reserach. I have always believed stock market speculators can learn a thing or two from shrewd horse race gamblers. And money management is one area I think we understand far better than the so-called white or blue collar investors from the world of finance--MBA's included! Prasad, a banker, has asked something to which I am not just replying in hollow words, but actually putting up a demo of the power of how a sound money management fromula, based on what I have learnt from horse race betting and its pitfalls, can give most rewarding results even in a market that crashed like a plane hit by missile.
Look at the shares, sheets, prices and buy/sell calls suggested by the formula, and just see how my formula delivers incredibly better results than the best money managers have perofrmed (?) during the three most stormy years between 2006 & 2008 (34 months between January 2006 & November 2008).
Dear Prasad (or anyone else from the stock market who reads this blog), please do not hesitate to contact me in case you have any queries, but remember my advice will come with a price tag, as I have absolutely no sympathy for stock market speculators who look upon us, horse racing gamblers, most superciliously with the least of reason.
Do focus on how the formula always manages to buy cheaper and sell higher to accumulate profits without letting the human ignorance, need, greed or fear come in the way of decision making. You don't even have to "think" if you should buy or sell at a particular price, the formula itself will tell you if you should buy or sell or hold (wait).
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