The Difference between Possible and Probable....

Hobart

This has been nagging at me for some time, infact I think I may have posted a thread somewhere here before about it, however this weekend it came to a head, so to speak.

My question is in regards to what is possible and what is probable. It basically comes from an idea about betting and the "perfect" bet i.e. one on which you cannot loose on. Here is an example:

Manchester United. They are a very good football team. at the start of every premiership season they have 38 matches to play. Nobody would give you odds on them loosing every match, however it is possible that they "could" loose every match, however it is not probable.

So the fact that they are never going to loose every football match in a season, does this not make it impossible, and if it makes it impossible could one not engineer a situation wherby you could guanantee to win money from a bookie on the basis that they will win at least once?

GuanYin

Yes you posted a thread on the perfect bet previously. It was an interesting one (that deviated slightly) so I've no prob with a repeat thread.

mr_angry

In my completely uneducated opinion, I would have thought that improbability would be an imprecise lay-mans term for something which had quite long odds. Possible hence becomes probable when the odds decrease to some unspecified value.

Hobart

mr_angry wrote:

In my completely uneducated opinion, I would have thought that improbability would be an imprecise lay-mans term for something which had quite long odds. Possible hence becomes probable when the odds decrease to some unspecified value.

I don't think that the "odds" would dicate in this case. As the difference between probable and improbable could lay with some other factors, when it comes to 2 teams playing a game of football anyhow! And also something, such as the result of a game of football could be both probable and inprobable, but never impossible, I would have thought.

Crumbs

To work on the basis that a certain football team will win at least once in a season, you could work on a betting system such as this:

1. Decide how much profit you want to make. Let's say €1000.

2. For their first match, place a bet so that you will make €1000 profit should they win. eg. They are at odds of evens, so you need to bet €1000. If they win, you've made your profit and you stop there.

3. If they lose, you now need to make back your lost €1000 plus the €1000 profit you want. Therefore, for their second match, you place a bet that will make you €2000 profit.

4. Repeat until they win a match and then you've made your net profit of €1000.

For the above system to work, you need a truckload of money in reserve should you need it and then there is the very small possibility that they might not win any of their 38 matches. It's not impossible, just very improbable...

Assuming their average odds on winning are 1/2, then the odds on them not winning all season would be (3^38)-1 / 1 = 1,350,851,717,672,992,088 / 1.

As you can see, very improbable, but still not impossible.

Pherekydes

Hobart wrote:

...could one not engineer a situation wherby you could guanantee to win money from a bookie on the basis that they will win at least once?

No! You will never guarantee to win a bet against a bookie. Betting is based on probabilities, and bookies' business is probability. They are the experts in that field.

Pherekydes

Crumbs wrote:

Assuming their average odds on winning are 1/2, then the odds on them not winning all season would be (3^38)-1 / 1 = 1,350,851,717,672,992,088 / 1.

Where did you get 3^38 from?

Isn't the probability of not winning one match 0.5?
And two 0.5 * 0.5 = 0.25 (0.5^2)

Therefore 38 matches:

0.5 ^ 38

The odds would be 274877906944 to 1

Hobart

Slow coach wrote:

No! You will never guarantee to win a bet against a bookie. Betting is based on probabilities, and bookies' business is probability. They are the experts in that field.

Even if I back, for example, Manchester United every week in a manner outlined by Crumbs above? Are you sure of that?

Capt'n Midnight

Don't forget that many bookies have limits on how much they will pay out on a bet, so if you fall behind you won't be able to keep going double or quits till you break even. Also like the tote the odds change according to how much is bet so that the no matter who finishes first the bookies rarely loose.

You would be much better off researching strange bets and thier probabilities, two examples , the guy who put a fiver on the UK Grand National being cancelled the third year, and betting on a hole in one being got on a major golf tournament as this happens every few tournaments and once upon a time you'd have got good odds on it.

If anyone has discovered a fool proof betting system then making it public is the fastest way of alerting the bookies to it and having it stopped p.d.q. cf. card counters in casinos, it's an arms race, figure out a better way and if you win too much you and your method get blacklisted.

Pherekydes

Hobart wrote:

Even if I back, for example, Manchester United every week in a manner outlined by Crumbs above? Are you sure of that?

Betting and probability are based on future events, so nothing is guaranteed.

If you can get a bookie to take your bet, i.e. that only one event of 38 has to come true for you to win your bet then take it.

You are making one fundamental error regarding probability: the opposite of losing is not 'winning'. The opposite of losing is 'not losing'.

Crumbs

Slow coach wrote:

Where did you get 3^38 from?

Isn't the probability of not winning one match 0.5?
And two 0.5 * 0.5 = 0.25 (0.5^2)

Therefore 38 matches:

0.5 ^ 38

The odds would be 274877906944 to 1

I was talking odds, you're talking probabilities.
Obviously they're much the same thing but they shouldn't be confused.

When I said odds of 1/2, I didn't mean a probability of one half (ie. 0.5), I meant odds of "1 to 2", which equates to a probability of two-thirds = 0.6666...

So if, on average, the probability of them winning any particular match is 0.666..., then the probability of them losing all 38 matches is (0.333...)^38, which is a very, very small number

= 0.00000000000000000074027370059729631731538525605465

= 1350851717672992088 / 1 (as odds)

Small probability = Long odds
Big probability = Short odds

The problem, I suppose, is using the division operator '/' to express odds rather than the ratio symbol ':' which I think would be better.

Finally, in my previous post, why was I calculating 3^38?
Because 3 = 1/(0.333...)

Pherekydes

Crumbs wrote:

I was talking odds, you're talking probabilities.
Obviously they're much the same thing but they shouldn't be confused.

When I said odds of 1/2, I didn't mean a probability of one half (ie. 0.5), I meant odds of "1 to 2", which equates to a probability of two-thirds = 0.6666...

Thanks for clearing that up. I assumed probabilities, my bad.

Crumbs wrote:

So if, on average, the probability of them winning any particular match is 0.666..., then the probability of them losing all 38 matches is (0.333...)^38,

You can't make that assumption. If the probability of them winning a match is 0.666..., then the odds of them 'not winning' is 0.333...

The odds of them losing a match would be something less than 0.333..., since they could also draw a match, which is also 'not winning'.

Crumbs

Slow coach wrote:

You can't make that assumption. If the probability of them winning a match is 0.666..., then the odds of them 'not winning' is 0.333...

The odds of them losing a match would be something less than 0.333..., since they could also draw a match, which is also 'not winning'.

You're right there. What I meant and what I should have said was "not winning" rather than "losing".

Capt'n Midnight

They are looking for a new Host for the Rose of Tralee.
You put a wad of cash down on Dustin, 'cos hes got good odds at the moment.
Then when you have the slip start a national campaign to have him become the compare, you get a couple of hundred thousand signatures and hey presto , easy money.

Don't forget that any scheme would also have to take into account draws , cancellations , clubs going into recievership and all those other things, if your margin is zero then you will loose.

rubadub

Hobart wrote:

Nobody would give you odds on them loosing every match, however it is possible that they "could" loose every match

If I was a bookie I would not give you odds on them loosing since it is very probable that it will not happen. If you bet €1000 and I only had to hand you over say 1c I am still wasting administration costs.

I am not sure if there is tax on gambling anymore but I think there was a time when if you won with very poor odds you would actually be down money due to tax being due on the inital bet +winnings (please correct me on that if wrong). Even if you find a bookie who states they will take "any bet" the odds will be set so low that it is not worth spending time going into the bookies. quicker to look for 1c on the ground

Hobart wrote:

So the fact that they are never going to loose every football match in a season, does this not make it impossible

no, it is still possible yet highly improbable.

The only sure bet I ever heard of over here was maggie shooting mr burns in the simpsons. People had heard about it from friends in the US who had seen it. Paddy Powers were taking bets at 500/1 at the start and a few guys cleaned up.

Hobart

I suppose I should have clarified more my belief that the sport is, kinda, irrelevant. Be it soccer, tennis, badminton, handball, roulette etc..... It don't matter. Pick the fav. Have a punt. If the fav looses, back him next time. Cover our original steak + new steak +factor in your accum. winnings. Eventually they will win.

Also the opposite of loosing is not always not loosing. It depends on the context and situation.

Capt'n Midnight wrote:

Don't forget that any scheme would also have to take into account draws , cancellations , clubs going into recievership and all those other things, if your margin is zero then you will loose.

If you just bet on soccer, yes. You could bet on tennis or any win/loose sport where a draw is not possible.

rubadub wrote:

If I was a bookie I would not give you odds on them loosing since it is very probable that it will not happen. If you bet €1000 and I only had to hand you over say 1c I am still wasting administration costs.

see above.

Pherekydes

Hobart wrote:

Also the opposite of loosing is not always not loosing. It depends on the context and situation.

Can you give an example. I don't understand. In terms of probabilities, if you give a certain event the outcome of which is E, then the opposite of that is 'not E'.

If I say it will probably rain tomorrow, then the opposite is 'not raining' (It doesn't matter if it's windy, sunny, still, cloudy -- they are all the one).

The opposite of losing is 'not losing' (winning or drawing).

Etc.

Capt'n Midnight

rubadub wrote:

quicker to look for 1c on the ground

I've heard they loose about £80m of change in the UK every year.

The way lotto's and casino's and bookies etc. work is they take money from everyone and hand some of it back to a few people which means they have to clamp down on schemes very quickly. And has been pointed out they have to pay for overheads and profit out of the take.

Another option it the tote. This works by sharing the winnings amongst the bets. So the more people who bet on a result the smaller the share they get, so it can be worth your while to put your money on placing rather than a win since there are less people to share the pool with. But a lot of people probably know this. The only thing in your favor is that the bookies won't care since the tote guarantees then never to loose.

Hobart

Slow coach wrote:

Can you give an example. I don't understand. In terms of probabilities, if you give a certain event the outcome of which is E, then the opposite of that is 'not E'.

If I say it will probably rain tomorrow, then the opposite is 'not raining' (It doesn't matter if it's windy, sunny, still, cloudy -- they are all the one).

The opposite of losing is 'not losing' (winning or drawing).

Etc.

Say I backed Marit Safin to win the Autralian open yesterday. I would have won the bet. The opposite of me not winning the bet is loosing the bet. Not not loosing, although you could say that not loosing = winning. However there are only 2 possible outcomes in a bet such as this 1. Loosing 2. Winning .

In your example of raining there are a number of physical outcomes, Raining, not Raining etc..... While technically not loosing could mean (winning or drawing). However if you construct a situation wherby you can only have 2 possible outcomes it is therfore logical to predict that the opposite of loosing is actually winning and not just not loosing.

Pherekydes

Hobart wrote:

Say I backed Marit Safin to win the Autralian open yesterday. I would have won the bet. The opposite of me not winning the bet is loosing the bet. Not not loosing, although you could say that not loosing = winning. However there are only 2 possible outcomes in a bet such as this 1. Loosing 2. Winning .

In your example of raining there are a number of physical outcomes, Raining, not Raining etc..... While technically not loosing could mean (winning or drawing). However if you construct a situation wherby you can only have 2 possible outcomes it is therfore logical to predict that the opposite of loosing is actually winning and not just not loosing.

In probability, the opposite of an event E happening is 'not E'.
If you start bringing in differing contexts you'll just get confused, as happened above. Obviously the number of outcomes will vary, depending on what event you're talking about, but when it comes to any event the following applies:

The event happens: E
The event doesn't happen: not E

Hobart

I am not disputing the rules of probability. I was merely commenting on the ascertion that the opposite of loosing is not winning, as put forward above. I was merely stating that "sometimes" and in certain contexts that is exactly what happens. The fact that:
The event happens: E
The event doesn't happen: not E

is true is not relevant to my original question, and I do not dispute.