I think that is what I did,or something similar,you see I did not believe the book solution was accurate.I assumed it an approximation.
I managed to get it to 0.039 and change.
My mate  has put it up on the web and managed to find half a dozen wizards who worked it out with all manner of methods.But the solution given beats them all hands down and,surprise surprise they all agree.
I am glad you like it.

Yes it must just be 3 consecutive so the 5,6 combinations do not count.

No ror,3 and only 3 consecutive as in the examples.
eg
1 8 12 13 14 23 counts but
1 8 12 13 14 15 would not count.
It is wicked,if I told you how long we worked on it you would die laughing.

No,exactly 3 consecutive so you have 3 consecutive and 3 singles ,so to speak.

I have had a go at 3 or more consecutive and that comes to,I think,0.041017 .
Someone put that up earlier and they must have got the answer to the original problem but not realised it.

ror,If I have understood you, I do not think that will work as you will still be left with sets comprised of 3 consecutive + 2 consecutive  + 1 solitary.
What we are looking for are the selections with only 3 numbers adjacent the remaining three must be solitary .

I can't work out the answer but I'm amazed at the amount of times dunlaying has to re-explain the simple question, even I understood it first time :)

Thanks Trev,I was beginning to wonder if I had not made it clear enough.
Here is the solution.
First we need to realize what we are after so let's look at the situation where we want 6 non consecutive numbers from the 49.
Clearly we need 5 "spacers" to make the 6 non consecutive.
It is not immediately obvious that this is the same as taking 6 numbers from 44,49 minus the 5 spacers.
It is however a fact and can be demonstrated to any one who understands (n)C(r) notation.
Once this is grasped it is easy to move on to the 3 consecutive problem.
Here we have 4 groups
3,1,1,1
1,3,1,1
1,1,3,1
1,1,1,3
therefore we will need 3 spacers.
You will be screaming by now that the foolish dunlaying has forgotten that we do not have identically sized groups.But,if we can abstract the spacers we can also do it for the 2 extra numbers that will make up our group of 3.We will then add them after to any one of 4 numbers to satisfy the rquired conditions.
Putting all this together we then have
4*(49-3-2)C(4) all divided by (49)C(6)
which is 4*(44)C(4)/(49)C(6)=0.0388...

Waht fro?

I'm not convinced the answer can be that symmetrical because of the following.

If your 3 in a row is 123 then there are 45 places the other 3 can go, but if your 3 in a row is 234 then there are only 44. Perhaps this is accounted for automatically but it feels odd the answer should then still be so neat.

Likewise when considering the individual ones, if you draw 27 and 30, there are more gaps the last cannot be than if you draw 27 and 29.

Perhaps this is accounted for by only specifying you need a gap, but again it feels strange!

I follow your argument though and it is convincing, it is just the boundaries that are worrying me.

Value was the origin of this tread and got lead onto a different path partly by me.
The same question is what and is value there, there  ?
For me yes as i have an advantage  as for most i do not think so.

I completely disagree. Maybe it is because I do sports betting not horses, but most the time I think the market is wrong is on short odds.

Quite often a price should be 1.17 but is 1.3 or something because the price is being held up, by either people trying to dictate the market or people laying to green out.

Either that or people underestimate just how dominant a favourite is. I've made good money this year laying little mix to be evicted from xf this year. I am essentially backing at about 1.1 that they stay but the real odds were much much shorter. Even had they ever been b2 they would have been saved against most others!

Provided they were VALUE odds

Backing at 1.01 BF odds...is generally "crazy"...................

I find it amusing how you think there are layers and backers on Betfair. There aren't, there are price makers and price takers.

Any time you take a price you arec giving away value to the person who made the price.

This is true whether you are laying or backing. The way to make money, (discounting in running) is to offer prices not take them.

Laying and backing are the same thing. If you lay team A to win you are simply backing the draw and team b in a dutched manner.

You say that football odds are different to horse odds, what does that mean? You're comfortable betting on a very likely event in football (the cs not coming in) but not comfortable betting on a likely event in racing (the horse winning, at similar odds.).

Here's a tip: if you are uncomfortable, then others probably are too, causing them to wrongly oppose the price. Doing what is least comfortable is usually a good indication of value.

Always stake sensibly, don't overstake, that is where people go wrong. If you usually bet £20, then bet it on the 1.02. Sure, you make 40p less commission, Profit is profit. Don't suddenly stake £1000 because you want to win a usual stake.

Again, if you think backing the 1.02 with a usual stake is "pointless" because of the lack of money then that means others aren't backing it for illogical reasons which again means price inflation. And that means opportunity and value.

Shorts odds backing is only the road to the poorhouse if you follow undern and his all in examples, but he is just demonstrating gambler's ruin.

It's only picking up pennies from under a steam-roller if you can't afford the down swings. Price in 10+  losses into your bank and you should find that short odds backing / long odds laying (remember these are the same thing!) can be very profitable.

. . and does your point apply to hooverers too?

Are they always giving away value because they are 'price takers'?!?

Ror,

Still have to disagree. Even pre-event, there are lots of quite significant mispricings to be found.

This occasionally can happen pre-off on injury/teams news, but I'm talking about punters just taking prices there, when you're better off putting money up on "the other side" and waiting. You'll get matched eventually unless you expect the market to correct.

I agree with you here, assuming that you're advising a recreational punter on what to do with his money. But someone who has actually priced up the event for themselves, and then discovered that the Betfair prices on offer are too large/small, should obviously take those prices.

I do this all the time on the football matches I trade, especially if I can see that the price has been moving in the direction that I consider to be the 'right' one. (So, I am less likely to get matched if I just leave an offer up).

ror 03 Dec 11 10:35 
Contrarian: I didn't word that well, I tried 3 times to write it.

You're giving away *some* value to the price maker. Hopefully you still have some left behind.

I also tried to say I'm talking about pre-event, not in-running. With in-running you have more information when you're taking than they had when making.

This occasionally can happen pre-off on injury/teams news, but I'm talking about punters just taking prices there, when you're better off putting money up on "the other side" and waiting. You'll get matched eventually unless you expect the market to correct.
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PRE-EVENT betting is more "understandable" re betting at such LOW ODDS......I agree.

IR betting at short odds ( I mean from 1.01 to 1.05)with HORSES would be "crazy" for punter on here who does not have "fast pictures" etc........

IR betting when say it is a NH race and you can clearly see a horse running well that , before the event you considered was a possible winner, and BACKING it at "good" odds makes far more "sense" than betting at the short odds end of market.( eg Drybrook Bedouin  was got at 25sBF odds IR in a 4 mile race approximately half way through race) NOW 25s is clearly VALUE compared to those BACKING at 1.01 to 1.05 near finish!

I don't need to run simulations to show that dutching all outcomes except 1 is the same as laying. It is so clearly true.*

*subject to outcomes not changing or presence of an any other.

Value is not subjective. There is an unknown true probability p_ and odds offered at p. The difference between these is value.

Whether or not their current value is positive or negative, by backing 1.96 in a 1.96/1.98 market, you are letting someone lay at 1.96. So they are getting extra value, whether or not you think their current value is positive or negative they get better value than if you put up a price and wait to get matched. If you put up a price then if it gets matched then you are getting better odds, which increases your value and therefore decreases theirs.

Going back to your final point, if you lay to a set liability, and if you believe in sensible staking you should, then there is no difference between backing a short odds runner or laying the rest of the field.

Again, I'm talking about sportsbook where you don't have non-runners messing things up.

BTO your maths fails you again.

Let us suppose that we have a market with 4 outcomes, A,B,C,D.

Let us also assume that the market is close to 100% overround.

Let us define a,b,c,d as follows.

Pr(A)=a, Pr(B)=b, etc.

Let us say you stake to a liability of x.

Wlog (without loss of generality) we can say a is the shortest odds.

Backing A means you win (1/a-1)x if it happens, lose x if it does not.

Now let us look at laying.

Let us have 3 lay amounts m,n,q.

Laying B to a liability of x means that (b-1)*m-n-q=x
We can substitute the same for C and D.
(c-1)n-m-q=x
(d-1)q-m-n=x

So how much profit does this generate on A?
m+n+q.

I've got to go now but I'll finish the proof later.