The Maths of betting

[Trader333]

temptrader,

Over what time frame would you consider proof that making money from betting on horse racing can be achieved ? Would 46 profitable months out of 49 be adequate and this is an approach based on backing not laying although it does require using a betting exchange ?


Paul

 

[grantx]

Pat,

I have a book called Fortune's Formula by W Poundstone. It's about various attempts to find solutions to betting, roulette, etc. It is mainly about an Americam mathematician, Claude Shannon, who devised gambling systems. The Art of War is my most boring book, this the second - once you put it down, you won't want to pick it up again.

Grant.

Grant.

 

[MrGecko]

Kelly isn’t particularly useful. Better than no risk calculation, but like most things pressed into service for trading purposes from external disciplines, it takes a significance way beyond its actual usefulness.

Bramble, I don't disagree that F* (Kelly) isn't the solution to all position sizing and portfolio management problems, but its a good start. We do have different ideas about how to actually work the thing out though - IIRC F* = (mean) / (Variance) of the probability distrubution of the event (i.e. the outcome of a trade). If one has enough data points (i.e. a comprehensive trade history), it would be possible to estimate these parameters with a certain degree of confidence to find F*, and then plug them into a MC simulation (and actually pretty simple to do in excel).

However, all this is slightly misplaced IMO. Problem I have with Kelly (and others) is that they don't (and cant, properly), take into account the discretion of a trader. The probability of a trade reaching pre-determined outcomes is different each and every time, and impossible to know in advance; the results of some optimisation sums done on old, irrelevant data are good for a framework but of little use in practicality.

To the OP; IMO it's essential that you have a solid understanding of what you are risking on any one trade, and going through the (rather laborious) task of profiling your system is part of it. Use your w:l, r:r, p:l, Beta and Alpha, all that jazz, to come to a benchmark figure of risk per trade (how you do it is up to you; if you try the Kelly method, use "half kelly" if you want to keep your sanity). Bear in mind, though, that the probability of your trade being a goodun' is different every time, and you can never know it for sure. You must rely on your judgement and position size accordingly - Kelly et al are good for strings of identical trades, but life isn't like that. For trades that you aren't 100% sure about, trade below your set risk level; For trades that you'd bet the ranch on, step up and trade a bigger size. If you've got it wrong, dont double up, go home.

As for the horse-racing thing, it seems to me there is a sure-fire way to win from the races - become a bookmaker.

 

[nine]

Mr Gecko,

A trick that could be applied is to take both the original series and the actual series and throw them into the Monte Carlo Simulator.

Actually at a very simple level when you had too few live trades you could just look at the impact of discretion on the trades and generalize that across the theoretical series. Once again they should be tossed into the sim.

To the OP, all the advice about kelly, half kelly etc (Sensible F instead of Optimal F) is good but its worth doing a Monte Carlo analysis as well. The crude statistics that appear when you mix up the orders of the trade series is a useful test.

 

[r.w.]

Hmm, the Kelly fraction has little to do with subjective a priori probabilities and more with the statistics of trading performance.

For example, a simplistic fx one, say you have a trading rule for entries with 20 pip SL and 70 pip TP and you move your stop to breakeven once you are at breakeven. Let's assume you get stopped out 3 times out of 10, stopped out at breakeven 5 times, and you hit 70 pips twice out of the 10. At one trade a day you earn 40 pips a week, and at 2% risk per trade your annualised return is 346% assuming 200 days in a year.

Suppose now that you change the MM rules to TP 20 pips. This means 7 winners out of 10, but still on average 40 pips a week. At 2% risk the annualised return is 376%.

So what? Well, up the risk to 5% per trade. The first system yields 2817% annualised, and the second 4165%. Why? Because the second system has higher Kelly fraction.

In conclusion, significantly increased annual return at the same average pips per week due to Kelly's idea. So it's not about the pips - cut the winners and up the leverage!

...sorry for the lecture, but hopefully helpful to some one-eyed piphunters.

 

[FXSCALPER2]

Obviously, you will lose regardless of what MM you use if you do not have an edge. If you have an ege, you are clearly better off betting more of your money (within limits) that less of it.

 

[Pat494]

Kelly isn’t particularly useful. Better than no risk calculation, but like most things pressed into service for trading purposes from external disciplines, it takes a significance way beyond its actual usefulness.

Can’t remember where I culled the following from (it was a long time ago), but happy to acknowledge any source that cares to claim it.

In answer to Pat’s originating question – there is absolutely nothing to stop you doubling or even Fibonacci-ing up on your trades, as long as you do so in equal proportion on both losing and winning trades and you have a positive expectancy for your system and your doubling/Fibonacci-ing doesn’t take you out of the game on drawdown. Kelly was/is a little optimistic suggesting you risk no more than 25% of your capital providing you have a max drawdown profile of 25%. Very optimistic actually.

The exact amount to risk on a trade is the big question in all money management systems. Risk too little will have your money won’t grow. Risk too much and the drawdown will put you out of business. In between too little and too much risk is an area where capital growth will grow to its maximum potential.

The original Kelly Formula was developed back in 1956 to solve a problem involving random interference on telephone lines. What Kelly discovered was a method of increasing data flow while reducing random information loss.

Before calculating the optimum percent to risk, you need your winning percentage (W%), the average size of your winning trades(W) and the average size of your losing trades(L).

The basic Kelly formula can be calculated as:

Optimum Risk Percent = W% – [(1-W%)/(W/L)]

Let’s have an example. Suppose you have a system that has a winning percentage of 0.6. Your system also has average winning trade of 8 and your average loss is 4. Thus, W% = 0.6 and W = 8 and L = 4.

Using these numbers results in the following:

Optimum Risk Percent = 0.6 – [(1 – 0.6)/(8/4]
= 0.6 – [0.4/2]
=0.6 – 0.2
0.4

Thus, the percentage of equity that would provide a maximum rate of return is 40%.

The major problem with the Kelly formula is drawdown. If you have a system that is right 60% of the time, you could still be wrong 10 or even 15 times in a row sometime during your lifetime of trading. Risking too high a percentage would be disastrous. The Kelly formula implies (sorry, you have to read the original report) that unless your drawdown is less than 25%, never risk more than 25% of you equity.

The Kelly Formula is critical for traders wanting optimal rates of return. For practical application of the Kelly Formula, use 80% of the Kelly %. In the above example – we derived an optimum risk size of 40% of capital. This is too high for practical use. Instead, we would use 80% of 25% which is equal to 20%. Determine how many trades you are likely to have on at one time and then divide your 80%-Kelly value by that number of trades. For example, if you are likely to have as many as 8 trades at one time, then your optimal trading size, using the above example, would be [20%/8] or about 2.5% of your trading equity.

Wish I had paid more attention in school during the maths lessons !
Thanks for all your answers. Still got the feeling that there should be some advantage here somewhere - but don't know where

 

[TheBramble]

Pat, to be fair, I didn't understand your initiating post. I only came in for the Kelly thing.

If you'd care to re-phrase or expand, perhaps you'd get a better response. Most folk, I think, thought you were talking about Martingale.

 

[temptrader]

Mathemagician and Paul,

I was talking only about back or laying (or both), but not trading or arbing. That's another matter entirely. There is definitely more people who are successfully trading on betfair - or arbing but it's getting awkward now - that there is, or ever will be, those that play the "proper" game of laying and/or betting based on form analysis. Of course we got to take off the possibility of crooked trainers going onto betfair and taking backs for the horses that they know will lose because they trained them to (the Keiran Fallon scandal involved a trainer with a 2 million pound betfair account).

If you look at all the tipsters Paul you'll see that, even the profitable ones, there's not that much money to be made there, and the drawdowns and years where they break even will put anyone off save for a few.

Let's cut to the chase: most people on this website want to become seriously wealthy, make money consistently etc . . . Backing and laying horses will not get them that because of the consequences of the probabilistic nature of the horses involved that accounts for the losing runs. Yet everyone poisons themselves thinking that this is possible. Unless your name is Mike Finlay, the chances are zero of you getting it to pay.

Let me give a stronger definition: a losing run is where you do everything that you were doing before that made you win, and not change a thing, and yet you still lose none the less. What is causing it is you playing probabilistically, but you can't help that, because the horse is the probabilistic factor that you cannot escape from. You can analyze form, jockey history, trainers records etc, everything you did before, and yet you will still lose. For this reason alone, ALL tipsters gets losing runs. And some of these losing runs wipe out the bank (or most of it). So you have to ask yourself: on my journey to making serious money should I ever want to deal with this kind of side effect that I literally have no control over?

 

[Pat494]

Pat,

I have a book called Fortune's Formula by W Poundstone. It's about various attempts to find solutions to betting, roulette, etc. It is mainly about an Americam mathematician, Claude Shannon, who devised gambling systems. The Art of War is my most boring book, this the second - once you put it down, you won't want to pick it up again.

Grant.

Grant.

Besides the fact the book is a bit boring did it give any insights ? My thoughts have recently been on a wave formation betting strategy.

 

[Mathemagician]

Let me give a stronger definition: a losing run is where you do everything that you were doing before that made you win, and not change a thing, and yet you still lose none the less. What is causing it is you playing probabilistically, but you can't help that, because the horse is the probabilistic factor that you cannot escape from. You can analyze form, jockey history, trainers records etc, everything you did before, and yet you will still lose. For this reason alone, ALL tipsters gets losing runs. And some of these losing runs wipe out the bank (or most of it). So you have to ask yourself: on my journey to making serious money should I ever want to deal with this kind of side effect that I literally have no control over?

I'm interested in hearing more of your thoughts on this.

jj

 

[TheBramble]

TT- I wont speak for trader333, nor do I need to, but suspect that was precisely his point. Money can be made, and is being made by trading and to a lesser extent, arbing, the horses on Betfair.

When I looked at it a while back (long while actually), there was edge there, but the volume then was too poor to warrant my long-term involvement. I couldn't get enough size on to make a worthwhile absolute profit for my efforts. Even trading ‘in play’ didn't afford the opportunity to substantially increase profits. The big Class 1 races were too few and far between where you could make a pig of yourself. That is just my view, based on experience from years ago.

I understand more recently, size has come into this market, but decidedly pro size and bias. The bookies are using Betfair to hedge their positions and to play size and spoof games that you or I would do exactly the same if we were in their position. It has made it, AFAIUI, rather more volatile and slightly more risky. If I had the time and capacity, I'd check it out personally to see if the extra volatility means greater opportunity considering the increased risk of pro involvement, but I'll leave others more currently qualified and involved to expand should they wish to.

 

[Pat494]

Pat, to be fair, I didn't understand your initiating post. I only came in for the Kelly thing.

If you'd care to re-phrase or expand, perhaps you'd get a better response. Most folk, I think, thought you were talking about Martingale.

Hi Bramble,
Perhaps putting it another way would make my question clearer.
If one had a 100% winning system ( obviously not possible ) one wouldn't need to have any sort of Martingale system.
Say one had a 90 % winning system. Even a doubling up system seems it may be near foolproof.
But for example a 75% winning system. How high in say doubling up would you have to go to get a 100% record on say 500,000 bets ? I was hoping someone might try it

 

[fifty2aces]

Let's cut to the chase: most people on this website want to become seriously wealthy, make money consistently etc . . . Backing and laying horses will not get them that because of the consequences of the probabilistic nature of the horses involved that accounts for the losing runs. Yet everyone poisons themselves thinking that this is possible. Unless your name is Mike Finlay, the chances are zero of you getting it to pay.

Let me give a stronger definition: a losing run is where you do everything that you were doing before that made you win, and not change a thing, and yet you still lose none the less. What is causing it is you playing probabilistically, but you can't help that, because the horse is the probabilistic factor that you cannot escape from. You can analyze form, jockey history, trainers records etc, everything you did before, and yet you will still lose. For this reason alone, ALL tipsters gets losing runs. And some of these losing runs wipe out the bank (or most of it). So you have to ask yourself: on my journey to making serious money should I ever want to deal with this kind of side effect that I literally have no control over?

We're on a trading forum here - whether you like it or not, trading is also a game of probabilities, and you can go on losing runs despite not changing anything. If you take a perfect long setup on the ES, and someone crashes a plane into a building in NY, you lose big. The market doesn't care about your system, and events are completely beyond your control. All you can do is take setups which you expect to be profitable, and exercise good enough risk management to avoid the downswings - same goes for betting on horses, poker, etc.

 

[TheBramble]

Hi Bramble,
Perhaps putting it another way would make my question clearer.
If one had a 100% winning system ( obviously not possible ) one wouldn't need to have any sort of Martingale system.
Say one had a 90 % winning system. Even a doubling up system seems it may be near foolproof.
But for example a 75% winning system. How high in say doubling up would you have to go to get a 100% record on say 500,000 bets ? I was hoping someone might try it

Probably me Pat, still not sure I’ve got it.

You seem to be suggesting that with any high Pw system (where Pw<100%), if you double up on losers they’ll ALL come good eventually?

To use your example, with a 75% Pw system, after 500,000 bets you will have won 375,000 of them and lost 125,000 of them. How would doubling up on those 125,000 losers have increased your profits? You would simply have doubled your losses.

 

[temptrader]

Bramble,

I have never argued with the fact that people are making money trading or arbing on betfair. That's just a blunt fact as far as I'm concerned. Trading the prices on betfair does not require you to know anything about horse racing.

I could join tipsters like Henry Rix (profits at about £25K for last year if I remember), but he goes through losing runs. And some years I believe he's just p*ss poor. He CAN'T make the game he's doing for millions. No, he has to get people interested in his services to make that kind of money.

Martingale systems can be used to increase strike rate of selections. They are also extremely dangerous. I know of one martingale system that uses selections that have 30 - 40% chance of winning and will produce a strike rate of about 95% in getting a winner at the end of the day going through those selections. This is an example where a 95% strike rate, as great financial cost, is not worth it in the long run. The system lasted for 2 months until a losing run of over 23 losers wiped out the bank. Again, the probabilistic effect messes things up.

Mathemagician, tell me how you calculate your losing runs and I'll humour you further. I take it you base it on historical data, or do you do worse case scenarios in your models?

Sorry fifty2aces, incorrect. That's why there are people making millions out of the stock maket and virtually no one doing so with the horses through form analysis. It goes against the grain to entertain the fact that losing runs can be virtually eliminated from trading. But then again, for someone to claim something like that, they must be a lair mustn't they?

 

[Pat494]

Probably me Pat, still not sure I’ve got it.

You seem to be suggesting that with any high Pw system (where Pw<100%), if you double up on losers they’ll ALL come good eventually?

To use your example, with a 75% Pw system, after 500,000 bets you will have won 375,000 of them and lost 125,000 of them. How would doubling up on those 125,000 losers have increased your profits? You would simply have doubled your losses.

I was suggesting that if one had unlimited funds one could double up losing bets until they win. Thus making a 100% winning system. Therefore the better your winning/losing% is then the less doubling up one would have to do.
So on a 75% win rate how much doubling up would one normally have to do to win every series of bets ?

 

[FXSCALPER2]

Hi Bramble,
Perhaps putting it another way would make my question clearer.
If one had a 100% winning system ( obviously not possible ) one wouldn't need to have any sort of Martingale system.
Say one had a 90 % winning system. Even a doubling up system seems it may be near foolproof.
But for example a 75% winning system. How high in say doubling up would you have to go to get a 100% record on say 500,000 bets ? I was hoping someone might try it

If your system wins 75% of the time and you double up after losses, you will go broke with a probability of 1. I am assuming you mean something like this: you risk, for example, 2% on trade 1 and you lose, then you risk 4% on trade 2, 8% on trade 3, etc. There will be no need for you to even think about what will happen after 500,000 bets. You will never survive long enough to get even close to that. About 5 losses will wipe you out.

If you want to optimise bet size, read and understand the Kelly criterion. You may still lose using Kelly but you will last much longer. That is even if you risk 10%.

 

[MrGecko]

Jeez................. :whistling

I was suggesting that if one had unlimited funds one could double up losing bets until they win

Theoretically, yes.

Thus making a 100% winning system.

If you don't include all the times you are wrong, you will end up being right sometime

 

[TheBramble]

I was suggesting that if one had unlimited funds one could double up losing bets until they win. Thus making a 100% winning system. Therefore the better your winning/losing% is then the less doubling up one would have to do.
So on a 75% win rate how much doubling up would one normally have to do to win every series of bets ?

There's one very erroneous assumption here Pat, that losing bets will at some point turn into winners.

They all don’t.

Especially in the realm of horse racing where there is a fixed end to the trade. In trading the market, you call the end (or your broker does). You don’t have that ‘luxury’ in time-finite bets.

It’s perhaps the illusion of infinite time that causes so many to lose so slowly in the markets. If they were all time-finite trades, those with a disposition to lose would be out of the game a lot quicker.

If traders were forced to realise their paper losses/gains in a market trade at a fixed point in time I wonder what impact that might have on folks’ risk:reward calculations?