trading question

for a start you never put your whole bank on one bet.

yes you are correct that if you back for £100 then you get £1 for every tick lower you lay at

back at 1.98 for £100 and lay at 1.90 would give you £8 (b4 comm) should that selection win. lay at 1.50 and you get £48 should that selection win.

yeah i was just using an example. but at what stage should you get out if odds start going against u??

You should get out when you think the current price is as good as you're going to get. If you don't know or you cant make an educated decision based on what is infront of you in your trading software then I'd suggest you're not ready to trade yet. It takes a long time to learn the markets well enough to give yourself a real idea of whats happening and what the best time to close your trade is.... even after years you can never be sure, theres no one single signal Im afraid :)

When you trade, all you're doing is making another bet, and if it's poor value then it will probably be detrimental to your profits.

I worded that wrong. What I meant was, bets are all about value irrespective of if you're 'trading'. I don't know why people talk about 'trading'. All you're doing is making another bet when you 'trade'.

When you're betting, risk is created out of thin air.
When you're trading, you are passing the risk onto someone else, hoping to earn a premium for yourself.

If you think a fair price for a selection is 4.00, it may make sense (depending on your circumstances) that if you have been able to lay at 3.5, you now back it at 3.95. Backing at 3.95 would not make sense for someone who is just betting.

The reason that this can make perfect sense for a trader is that the decrease in variability of returns that he achieves by 'giving up' a little of his value, means he can comfortably bet a larger proportion of his bank, meaning that the smaller edge, leads to larger profits.

Once his bank is large enough, it could make sense to place value bets instead of giving up a little value by trading out, but the other factor to consider is that this leads to larger commission costs.

Simple remedy to that is not overstaking the first place. Then you can concentrate on value and thereby optimising your edge.

in the first place

The Investor Joined: 05 Jun 06

If you think a fair price for a selection is 4.00, it may make sense (depending on your circumstances) that if you have been able to lay at 3.5, you now back it at 3.95. 


Makes it far easier to spin your money over and over as well

The advice from the Investor is spot on, say you have laid a side at 3.5 following a goal, and the current price almost instantly resets to 3.95/4.0, it is perfectly sensible to green out at what is more or less the correct price, very few could estimate exactly if it should be 3.95 or 4.0 or whatever, but taking a profit or at the very least getting your stake back at "approximately" the correct price is almost never wrong, as stated anything which reduces variance and damage to your bank has to be correct, other things being equal.

The way Betfair is designed, it doesn't make sense to bet rather than trade if your aim is to maximize profitability.

Betting on betfair (as opposed to trading, arbing etc.) only makes sense if liquidity is poor and trading out of a position is difficult. There are no exceptions. If you can place a value bet, and then trade out of the bet at fair value, this should always be done.

If the above scenario was a real one, a value bettor would only be able to put about 10-12% of his bank on this bet, whereas a trader would comfortably be able to put on as much as 50% of his bank (if it was a pre-off early match odds market that will get high liquidity later for example), and completely trounce the value bettors' returns.

If you have to reduce the variance, you just stake less. Simple. Then you can focus on finding good prices rather than 'greening out' at a bad price because you're sh*tting yourself about your liability. It's just another bet. It's a complete fallacy to believe you're giving yourself a free bet.

Yes it's simple if you are content with a lower return.

Another thing a bettor can't do that a trader can is profit from a small edge. In 2009 my return on turnover was less than 2%. If I was getting that without trading, it would be a net loss, when In fact, I had a 52 consecutive week run without a losing week, and paid PC in more than 30 of those weeks.

If I was limiting myself purely to big value bets, I would have made less with more volatility.

Another point to think about...


Assume  you Lay a football club  to win the Euro 2012    at odd of 21 to 1  or higher...  (eg france)


If  that team  gets  to the Final.
Will the Lequidity  to unwind  your bet   go up or down??      (regardless of profit).

lol Investor. Or you could just make a bet for the same liability that would be created by that trade. It's not a sly way of getting a bigger bet on you know!

ps,  "The Investor"  right...

I think Rowan may be missing the important point that Investor is making about the profitability effect of netting off positions within a series of bets on the same event. It is an important one to focus on.
One off value bets going one way only are very inefficient commission wise, unless of course your value calculations take into account fully the commission factor ( which they should ).

I think it is a way of getting a bigger bet on.

For example, on some events, I've had a total liability of lay bets of around £200-£300k. Of course I was laying, then backing, laying then backing on and on, as I don't even have anywhere near to that amount in my account.

If what you are saying about commission is true, then that is completely valid point, but doesn't the commission charge work out the same?

"I think it is a way of getting a bigger bet on.

For example, on some events, I've had a total liability of lay bets of around £200-£300k. Of course I was laying, then backing, laying then backing on and on, as I don't even have anywhere near to that amount in my account. "




**   I can only  assume  your not doing that kind  of Vol  on one football match!
-  Even  at  10K  per trade,   thats  20 to 30 trades.   ???

FINE AS FROG HAIR Joined: 12 Mar 07
Replies: 364 30 Aug 10 20:50   
I think Rowan may be missing the important point that Investor is making about the profitability effect of netting off positions within a series of bets on the same event. It is an important one to focus on.
One off value bets going one way only are very inefficient commission wise, unless of course your value calculations take into account fully the commission factor ( which they should ).


I've just calculated that it makes no difference. Do you have Excel? I made an Excel spreadsheet based on exactly how Betfair charges commission on trades and single bets. If you go down to the 'reduction factor - win market' section of my spreadsheet you'll see where I've entered an example of a 1.5 to 1.2 trade and a 1.2 single back. I chose these odds because backing at 1.5 and trading out at 1.2 for an equal profit on the 1.5 back winning or losing equates to a 1.2 back. Download it here:

http://rapidshare.com/files/416103628/BARUALATOR_V._8.31_Trade_Example.xlsx

You'll see that profit is the same irrespective of approach.

Whoops. Ignore that. I didn't enter a stake for the 1.2 back. I'll upload another file in a second.

OMG. FINE AS FROG HAIR. You are right!!!

MIB34, If I lay a correct score of 0-3 in Man U v Wigan at say 500, a £10k liability on my side, would only show up as £40 matched on Betfair (£20 backers stake x 2)

Download that spreadsheet, and clear the trade and then enter a stake for the 1.2 back. You will see that Frog Hair is right!!

Trading is good, but not for the reason Investor has offered.

What are you talking about? What's wrong with what I said?

Or is that what you meant Investor?

Yes, that is an important part of what I meant.

Oh right! Pleased it makes sense now.

I've just noticed that you made the point about commission as an additional point. I think that's the only important point.

If you ignore commission, then it's not a way of getting a bigger bet on. The point you make about commission is true though, and proves that trading is worth doing. I've never thought about that before.

In theory you could make a fortune quite literally by trading a single market, starting with an arbitrary small sum. This would not be possible for someone who just places some bets in the market.

back at 5, lay at 4.9, do this x of times with the same selection, and you could make a return as large as you like. How can you say it's not a way of getting a bigger bet on?

I'm using an exaggerated example deliberately to make it clear what I mean.

Rocket to the FACE Joined: 28 Oct 08
Replies: 5554 30 Aug 10 20:23   
The Investor Joined: 05 Jun 06

If you think a fair price for a selection is 4.00, it may make sense (depending on your circumstances) that if you have been able to lay at 3.5, you now back it at 3.95. 


Makes it far easier to spin your money over and over as well

^
exactly.

that was a quote of me replying to a quote of you earlier on

but anyway, the investor is right.

"If I lay a correct score of 0-3 in Man U v Wigan at say 500, a £10k liability on my side, would only show up as £40 matched on Betfair (£20 backers stake x 2) "


FAO,  The Investor..       Thats  exactly  what I assumed  you were doing!    ;)



I couldn't  see you doing   200,000     One pound trades  per match.




Dont get me wrong,   10 pc's   a selectio of bots,  a decent server,  and  alot of band width     and  entering the  200+  trades per football match  i can understand!


(Me  im more of a  3  or 4 trades  per yer  type).

Hmmm. Maybe you're right Investor. I'll have a look at that and will say what I think.

I'm sorry for misunderstanding you Investor. I'll have a good think about what you've said.

Unfortunately, I've changed my mind on this again with regard to commission.

Say you back at 1.5 and lay at 1.2 for equal profit on the 1.5 back winning/losing, that's equivalent to a 1.25 back right?

I've found that profits are the same after commission irrespective of approach.

If you've got Excel, download this spreadsheet that I made and go down to the 'win market - reduction factor' section where you can enter trades and see what your book looks like after commission based on exactly how Betfair charge commission. I have entered a 1.5 to 1.2 trade already, but look at the profit it calculates, and then clear this trade and enter a single 1.25 back for the same stake and you'll see that profit is the same after commission imo. Although I suspect I'm missing a subtle detail again.

BTW, I think is quite a useful spreadsheet, and I would like you to download it and give me some feedback please. I designed it for primarily for dealing with late horse racing scratches:

http://rapidshare.com/files/416128712/BARUALATOR_V._8.31_Trade_Example.xlsx

I'm sure you're right though Investor, I'm just sceptical again. I'm probably missing something.

The Investor
Joined: 05 Jun 06
Replies: 2362 30 Aug 10 21:36   
In theory you could make a fortune quite literally by trading a single market, starting with an arbitrary small sum. This would not be possible for someone who just places some bets in the market.

back at 5, lay at 4.9, do this x of times with the same selection, and you could make a return as large as you like. How can you say it's not a way of getting a bigger bet on?


I see what you mean now. I didn't realise you meant repreatedly trading. You're right, it's a way of effectively getting your money back and then putting another bet on.

I disgaree at the moment about the commission benefit though.

I was confused by the wording of what you said, because literally, it's not a way of putting a bigger bet on, it's a way of making more bets on the same market with the same amount of funds.

Although, I suppose if the price kept moving back and forth on pre-event, then you would be putting a bigger bet on! lol.

Sorry to multi-post so much, but I keep re-thinking things! LOL

I think Victor's good value for Big Brother.

13.5 at present

Say you back at 1.5 and lay at 1.2 for equal profit on the 1.5 back winning/losing, that's equivalent to a 1.25 back right?

The big difference is that if the trader doesn't win in your example, he doesn't lose either, whereas the bettor does.

I think the simplest thing to do is a simulation.

Have a a look at this, it's a series of 1000 bets (or 2000 for the trader as he both backs and lays.).
http://rs513.rapidshare.com/files/416236533/bettor_v_trader.xlsx

Hit an empty cell and press delete and a new random set of data pops up.
A bettor and a trader start with a bank of £100. The bettor repeatedly backs at 4.5. The trader lays at 4 and backs at 4.4.
The fair price is 4.

They are placing these bets on the same events with the same stake / proportion of bank, so the bettor by definition has a larger edge.

This is not quite realistic, as it is an overly simplified model, but it should explain the commission benefit, as well as showing why it is worth sacrificing profit (edge) to stabilize returns.

Although the bettor makes more on average in this example, the trader could easily stake 10-20 times as much (he could stake everything each time in this example, but I mean in the real world).

For a bettor, luck plays a more significant role than for the trader.

Thanks Investor. I'll look at that. It makes sense that you can get more bets on as a trader, I'm still not sure about the commission charge.

If I put £100 on a 1.25 shot, I stand to win £23.75 at 5% commission.

If I back a 1.5 - 1.2 trade to occur with £100, and I get the trade, my profits are £23.75 after 5% commission.

Test it using this:

http://rapidshare.com/files/416128712/BARUALATOR_V._8.31_Trade_Example.xlsx

Maybe I'll understand after I look at the spreadsheet though.

Betfair charge commission on your net potential profits after the trade has occured.

Good spreadsheet Investor. :) You should download mine. I'm enjoying studying this.

Hmmm, your spreadsheet charges commission in the correct way, and demonstrates a commission benefit from trading, so you must be right. Just trying to work out why it works now. Good job Investor.

Investor. Surely the average commission charge is only smaller when you trade because those 4.4-4.0 trades are effectively 1.10 backs? Of course the commission charge is smaller when your average wins are smaller. I've noticed that there are times when the bettor absolutely hammers the trader. I'm pretty sure there is no benefit from commission, but your point about being able to effectively get bigger bets on through trading seems plausible so far.

lol. I found instance where the bettor wins over £1000.00. Just looks like swings and roundabouts to me, or in fact the bettor does better on average he/she doesn't back at 4.5 rather than 4.4.

Backs at 4.5 rather than 4.4 I mean.

Sorry for the multi posts, but I keep coming up with new things. Surely your simulation makes an unfair assumption that the 4.0-4.4 swing always occurs.

If we assume the prices are fair when they appear, then that swing is expected to occur 90.91% of the time.

Actually, I retract my last comment. That is a fair assumption, because it's offset by the assumpting that 4.5 always appears for the backer, so it is fair.

You say luck that the bettor is more reliant on luck. Why so? Long-term the trader is more vulnerable to luck because the trader is making worse bets. Sure the trader gets more wins, but the trader is effectively backing 1.10 shots, so therefore needs a lot more wins.

Your simulation emulates a situation where a 4.0-4.4 swing is guaranteed, so effectively 'free money' is available, which is gold dust, but whilst the trader settles for guaranteeing a consistent profit, the trader optimises his/her long-term profits by just backing the 4.5's that always appear. The bettor risks losing all his/her money, but the bettor expected p/l is superior to the trader's.

Commission charges are the same for both entities, as they are both charged 3% on their profits.

The bettor* optimises his/her long-term profits..

The whole thing rests on having an edge, so in a sense you could call that free money.

The 'free money' is available to the bettor and the trader in my example. Just imagine that this is  a game where the odds of winning on each round are 25%. You have a built in advantage because you can either back at 4.5 or lay at fair odds and back 4.4.

In reality the trader's returns would be a little more volatile, but what it shows is that if you are making money by betting and getting value, you should trade out of positions if you can do so at a fair price (or even slightly worse than fair).

Don't forget the critical point that the bettor and trader are staking the same amount (1% of bank). The trader could easily stake 20% of his bank on each trade, whereas the bettor would go broke with a very high degree of certainty if he tried this.

What I meant by the bettor being more reliant on luck is that after 1000 bets, he could have made a 1000% return, or he could have lost half his capital. Imagine you had 100 traders pursuing this strategy, and 100 bettors pursuing it. They all adhere to the staking given in the spreadsheet, and place bets on different markets from each other, but with the same edge. The traders would all make a similar amount, whereas the bettors' results would vary greatly, purely due to luck. For instance lets say some of these make £1,000 as you pointed out, others make very little or even lose money.

What I meant by 'luck' was that the huge differences in profitability for bettors have nothing at all to do with skill.

Ye but what about Victor.

I'm aware of the scenarios, and I have said that your theory on the trader being about to effectively get more on through 'spinning' his/her money, is an advantage, but ignoring that, the bettor's expected p/l is bigger than that of the trader.

You are right that in this scenario, the trader guarantees themself a certain profit through exploiting the price swing, which we know is going to occur, and the bettor does not guarantee that, but the bettor still made the best investments even if he/she lost all their money.

Obviously in practice we would not know for certain that the price swing is going to occur, but it's perfectly fair to assume it is for the purposes of this simulation.

trader being able* to

What I meant by the bettor being more reliant on luck is that after 1000 bets, he could have made a 1000% return, or he could have lost half his capital. Imagine you had 100 traders pursuing this strategy, and 100 bettors pursuing it. They all adhere to the staking given in the spreadsheet, and place bets on different markets from each other, but with the same edge. The traders would all make a similar amount, whereas the bettors' results would vary greatly, purely due to luck. For instance lets say some of these make £1,000 as you pointed out, others make very little or even lose money.

A 4.4-4.0 trade equates to backing a 1.10 shot, so effectively all you're saying is that a group of people backing 4.5 shots will have a greater p/l variance than a group of people backing 1.10 shots, but where n='number of bets made by both parties', as n tends to infinity, that variance tends to zero.

The Investor Joined: 05 Jun 06
Replies: 2367 31 Aug 10 14:41 

Say you back at 1.5 and lay at 1.2 for equal profit on the 1.5 back winning/losing, that's equivalent to a 1.25 back right?

The big difference is that if the trader doesn't win in your example, he doesn't lose either, whereas the bettor does.


That's just aftertiming. When you back the 1.5 shot, hoping to trade out at 1.2, assuming prices are 'true' when they appear, the probability that you will get a chance to trade out at 1.2 is 80%, which is exactly the same as the probability of a 1.25 shot landing, assuming the 1.25 is the 'true' price.

but the bettor still made the best investments even if he/she lost all their money.

I think that highlights where we disagree [;)]

@Rowan86


Would you do a betting strategy  IF  you made a loss  90%   of the time  ?

OK Investor. A series of guaranteed, disproportionate 4.4-4.0 swings are going to occur in the near future, as well as some disproportionately big 4.5 shots. I'll back the 4.5 shots. You make the trades. I'll probably make more money than you unless you do your trick where you get extra bets on, but to be honest, I could just make extra bets too as long as I have more funds than you available. :)

MIB34 Joined: 24 Nov 07
Replies: 25 31 Aug 10 21:07 
@Rowan86


Would you do a betting strategy  IF  you made a loss  90%   of the time  ?


A betting strategy? My strategy involves finding value. Nothing else. Would I back 15.0 shots that lose 90% of the time? You bet I would!

:)   Good.   Many people wont!

lol. Right.

You would make more than me on average by taking excessive risk. To me taking this risk isn't worthwhile. Would I prefer £100,000 to a 1 in 10 chance of £1,050,000. yes.

If you wanted to, you could back at 4.5 with your whole bank all in your initial £100.
After 8 rounds, you would have a 1 in 65536 chance of getting 168151.3 times your money back. That's still a good deal, and I would happily put £100 up if someone offered this to me, but if I had the option of trading for an (almost) guaranteed smaller profit, I would take it.

Risk isn't just something to ignore, reducing it has a real monetary value, although it's not easily quantified.

The Investor is right and I would add that accurately predicting the volatility of a market is a crucial piece of information. It's how I make most of my money.

There are two possibilities.

1. This situation where we know 4.4-4.0 swings and 4.5's are guaranteed is a one off in which case it could be deemed that as a gambler, it's the trader taking a bigger long-term risk, because he/she is failing to fully exploit the situation.

2. This situation is going to be available for an infinite length of time in which case the trader will beat the bettor long-term because by the nature of infinity the bettor will eventually lose all his/her money.

This situation would never occur in practice, and the trader would never be taking less risk. You need a strike rate better than 90.91% to make 4.4-4.0 trades profitable. That offers no advantage over someone backing 1.10 shots and letting them ride.

The is Never  enougth  Liquidity  when you need it. !

Rowan86 Joined: 13 Jan 05
Replies: 1184 01 Sep 10 21:11 
There are two possibilities.

1. This situation where we know 4.4-4.0 swings and 4.5's are guaranteed is a one off in which case it could be deemed that as a gambler, it's the trader taking a bigger long-term risk, because he/she is failing to fully exploit the situation.

2. This situation is going to be available for an infinite length of time in which case the trader will beat the bettor long-term because by the nature of infinity the bettor will eventually lose all his/her money.

This situation would never occur in practice, and the trader would never be taking less risk. You need a strike rate better than 90.91% to make 4.4-4.0 trades profitable. That offers no advantage over someone backing 1.10 shots and letting them ride.


First you need an edge. Without that all of this doesn't matter.
Second how do you exploit that edge most efficiently? Let's say we decide that a fair price for a selection is 4. We know from experience that if we lay at 3.5 and/or back at 4.5 in a market that will be reasonably liquid at some stage before the event, the chance we will be able to trade out at a profit if we get matched is extremely high, as is the allowable margin of error. Profit for a trader in this situation will be extremely stable.

The whole thing is dependent on the amount of money available to you. If you have £10k in your account, and can only get £20 on at 4.5, it may not make sense to lay at 4.1 and guarantee the profit. But even if you had £500k in your account, it would always make sense to lay at 4, lowering volatility and commission.

If you have £10k in your account and can get £2k on at 4.5, trading out at 4.1 (or any price you can get under 4.5) makes perfect sense, as the risk level of a £2k straight bet would be intolerable.

We know from experience that if we lay at 3.5 and/or back at 4.5 in a market that will be reasonably liquid at some stage before the event, the chance we will be able to trade out at a profit if we get matched is extremely high, as is the allowable margin of error

That works out as about a 1.29 shot.

If the swing occurs more than 78% - heaven.
If it occurs less than 77% - dog house.

That's ignoring commission.

It's the same with backing 1.29 shots and letting them ride.

Staking £100 on a 1.29 shot, and

risking £100 on a lay at 3.5, hoping you can trade out at 4.5 for even profits on the 4.5 shot winning and losing is effectively the same thing.

I got that COMPLETELY wrong. I foolishly assumed that backing a 4.5 and trading out at 3.5 would work out the same as laying a 3.5 and trading out at 4.5.


laying 3.5 and then backing 4.5 works out at about a 1.09 shot.

Let me rephrase what I said earlier about the trader 'hoping' to be able to trade out. It is more an educated guess than a hope. The swing will occur more than 85% of the time if someone knows what they are doing. They will be able to trade out more than 95% of the time at the price they got in or slightly better. That leaves 5% where they need to take a loss.

Ok, I just kind of guessed that, but it's common sense that if 4 is a fair price, and you manage to back at 4.5, the chance of your lay getting matched if you offer a price better than four is extremely high, I don't see how a 1.29 shot comes into it, that would only be relevant if you were blindly betting 'hoping' that this swing occurs, when it is highly predictable that it will.

I never said it was based on hope necessarily. What makes you think an educated guess on a 3.5-4.5 swing occuring is superior to someone that's good at gauging 1.09 shots?

If you're brilliant at predicting 3.5-4.5 swings, bully for you, but you're no better someone that's outstanding at landing 1.09 shots.

That example you just offered is a scenario where you're lucky enough to get a 4.5 shot that should be 4.0, and then you're using that fortune to say that your trade is clever. The only clever part was backing 4.5. You're right. Given that you know it should be 4.0, the probability of your trade landing is disproportionately high, but that owes itself to the fact that you took value at 4.5 as much as anything.

Rowan86 Joined: 13 Jan 05
Replies: 1189 02 Sep 10 01:43 
If you're brilliant at predicting 3.5-4.5 swings, bully for you, but you're no better someone that's outstanding at landing 1.09 shots.


No better perhaps, but my profits will certainly be more stable.

I want to find a point of agreement with you Investor, as this has been a great discussion, but there's really no difference. You'll need those 3.5-4.5 swings to land more than 91.7% of the time just like you'll need that strike rate backing 1.09 shots. I nearly agreed with you at one point. You were convincing, but unfortunately, I just think it's swings and roundabouts.

Your point about being able to get more bets on the market through trading is true though.

Why would your profits be more stable?

You back the swing to occur and it doesn't, so you lose £x.
You back the 1.09 shot to win and it doesn't, so you lose £x.

Potential profit the same in both cases with same liability.

Rowan86 Joined: 13 Jan 05
Replies: 1189 02 Sep 10 02:04 
[...]
You're right. Given that you know it should be 4.0, the probability of your trade landing is disproportionately high, but that owes itself to the fact that you took value at 4.5 as much as anything.

I'm certainly not denying that. You could draw a parallel with an insurance company. It makes money by setting the 'odds' that they will have to pay out, and collecting more in premiums than they pay out.

It can maximize it's profits by buying insurance from a reinsurance company. Obviously the reinsurer profits from this, so the insurance company is giving up part of it's 'edge'.

This allows it to take on more risk (larger bets). Effectively this company is now trading rather than betting. The reinsurers tend to be much better capitalized, so the smaller 'direct' insurance companies can tap into some of that wealth in this way. Almost all of them choose to do so.

(The only legal distinction between a bet and an insurance contract is that one is not a hedge against a negative impact event and the other is)

OK, but the point is that that scenario doesn't represent a victory for trading. It's a victory for value seeking.

I'm not getting this profit-stabilising concept. I think you just like backing things that have a high probability of winning. There's no basis for saying that your profits are more stabilised backing 3.5-4.5 swings than if you back 1.09 shots. Your liability/ potential profits are the same with both approaches.

I really don't understand your idea of it being the same as backing 1.09 shots?

OK then.

Lay 3.50 for £250 liability to win £100.

Back 4.50 with £77.78.

You win £22.22.

Not a lot different to backing a 1.08888 shot with £250 to win £22.22.

I've just written a mathematical proof that if we assume that prices are always available and always represent the 'true' price when they appear, the probability of being able to trade out at 4.5 after laying a team at 3.5, is around 91.8%, which is the same as the probability of a 1.0888 shot landing assuming it represents the true price.

I can post it if you're interested.

Yeah post it.

I agree with your conclusion. It's the underlying assumption that's different. I assume that when my bets are matched, they are more likely to be in my favour than not. Working from that assumption, you'll probably see there is a big difference.

Yes. WHEN they're matched. That's like saying a 1.09 shot is in your favour once it's won.

Or when you get a bet matched at good value, you're quite often close to the finishing line because you have a disproportionately high chance of trading out, but that's a bit like backing a good value 1.09 shot.

In a football match, if we assume that prices are always available and always represent the 'true' price when they appear, the probability of being able to trade out at 4.5 after laying a team at

3.5, is around 91.8%.

Proof:

Where

pr(x) = probability of x occuring
pr (x/y) = probability of x occuring given that y definitely occurs


Where

x = team wins
y = 4.5 appears


By the law of total probability,


pr(y) = pr(x)*pr(y/x) + pr(x doesn't occur)*pr(y/x doesn't occur)


pr(y) = (1/3.5)*pr(y/x) + (1 - (1/3.5))*pr(y/x doesn't occur)

pr(y) = 0.2857*pr(y/x) + 0.7143*pr(y/x doesn't occur)


pr(y/x doesn't occur) = 1, because if the team doesn't win, it is certain that 4.5 appears, given our assumption that prices always represent the 'true' price when they appear.


pr(y) = 0.2857*pr(y/x) + 0.7143


By Bayes Theorem,


pr(x/y) = pr(x)*pr(y/x) / pr(y)


Rearranging gives,

Pr (y) = pr(x)*pr(y/x) / pr(x/y)


Substituting pr(y) for previously derived equation gives,

0.2857*pr(y/x) + 0.7143 = pr(x)*pr(y/x) / pr(x/y)


pr(x/y) = 1/4.5 = 0.2222


0.2857*pr(y/x) + 0.7143 = (1/3.5)*pr(y/x) / p(x/y)

0.2857*pr(y/x) + 0.7143 = 0.2857*pr(y/x) / 0.2222

0.06348*pr(y/x) + 0.1587 = 0.2857*pr(y/x)

0.2222*pr(y/x) = 0.1587

pr(y/x) = 0.7142


Substituting pr(y/x) into previously derived equation gives,

pr(y) = 0.7142*0.2857 + 0.7143 = 0.9183 (91.8%)


Pr(1.09 shot winning if fair price) = 1/1.0888 = 0.918 (91.8%)

Good night Investor mate. I'll check if you've posted tomorrow night.