E = Dr x Pw – R x Pl

[crash]

In plain English, this says that your edge is equal to the amount of money you can potentially win [odds], times the probability of winning [your hadicapping or system], minus the amount of money you place at risk [your bet], times the probability of losing [the remainder after your probability of winning].

Everything we do in horse race betting is wrapped in that little equation. We just have to worry about four little things: improving handicapping, improving odds, improving betting strategies, and decreasing losses. This shouldn’t take very long ….......

[KennyVictor]

Better give us an example using plain numbers instead of plain English I think Crash.
KV

[jfc]

Better give us an example using plain numbers instead of plain English I think Crash.
KV

KV,

You attempt mathematical modelling of various gambling strategies. So it is disturbing that you cannot figure that Crash's formula is actually a simple version of Expectation.

I consider that Expectation is second to no other concept in risk/reward evaluation.

While I knew about the originator of Expectation, until now I didn't realise that he introduced it in the first ever published book on probability.

Here is that original 1657 work conveniently translated from the Latin:

http://math.dartmouth.edu/%7Edoyle/docs/huygens/huygens.pdf

And here is a rework and attempted explanation is modern language.

http://www.math.dartmouth.edu/~doyle/docs/hedge/hedge.pdf

While life is too short to more than browse through what most people should already kinda' know, it does give an insight in how people started to think about probability.

And it bears an eerie resemblance to the concepts required in Exchange Betting.

[KennyVictor]

Hi jfc,
English is such a well developed language. It's almost infinite subtelties allow us to express such finely honed nuances of meaning with the changing of a single word. The single word you've stumbled over here, jfc, is "us".
When I read Crash's formula I spent a few seconds on his explanation and, as I expect you already realise, knew just what he was expressing but then I wondered if he'd been drinking from the same cup of pedantry that you so heavily quaff on occasions. What about the poor Joes that can't understand this I thought, don't they deserve to learn. I suppose I could have said "Better give the dullards an example.....", or "Better give the mathematically challenged an example...." but no, that would be cruel and I'm not too proud to lump myself in with the common man "Better give us an example....." is so much more friendly.
But anyway, I'll assume you though I was using the Royal "us" so thanks for helping us mere mortals by simplifiying the whole thing for me. :)

KV

[crash]

From one Joe to another Kenny, although my formula has a mathematical basis and is a simple truth, it was presented as a bit of everyday humour as I'm sure you, jfc and anyone else who read the post were aware off [?].

The 'cup' I quaff from is more horse trough than fine pedantry china :-))

[crash]

Sooooo, for this humble trough drinker who has just finished reading about 'expectation' from:
http://www.math.dartmouth.edu/~doyl...hedge/hedge.pdf is it right that the chance of a horse winning a race in a 10 horse race is 1 in 10 and the chance of it placing in the first 3 is 3 in 10, but if I choose 3 horses to place boxed [a simple boxed tri], my chances are 30/1 as in the below table or am I wrong?



QUOTE:
Peter's gamble
Peter asks me for a bid on the following gamble. I get to
flip a coin up to 10
times. If I get heads on the kth
flip, 1 . k . 10, I collect 2k1 and stop. If I
manage to
flip tails 10 times in a row, I collect 1024.
How much should I offer Peter for this gamble? In theory, the value of
this gamble is
· 210
(1=2 · 1 + 1=4 · 2 + 1=8 · 4 + :::+ 1=210 · 29) + 1=210
= 10 · 1=2 + 1
=6.
This means that with the aid of side bets, I can in theory arrange to net 6
from this gamble no matter what. Here's how it might go: On the first
flip, I'll make a side bet on heads with Laurie, for 5. If I flip heads, I'll collect 5 from Laurie and 1 from Peter, so I'll wind up with 6, as promised. If I
flip tails, I'll pay 5 to Laurie, making 5

Flip Side Bet Heads fortune Tails fortune
1 5 5+1=6 -5
2 9 -5+9+2=6 -5-9=-14
3 16 -14+16+4=6 -14-16=-30
4 28 -30+28+8=6 -30-28=-58
5 48 -58+48+16=6 -58-48=-106
6 80 -106+80+32=6 -106-80=-186
7 128 -186+128+64=6 -186-128=-314
8 192 -314-192+128=6 -314-192=-506
9 256 -506+256+256=6 -506-256=-762
10 256 -762+256+512=6 -762-256+1024=6
END QUOTE.

[Chrome Prince]

Isn't it wonderful how some scientists and mathematicians turn simple theory into blithering shortcuts and Bachelor of Mathematics speak.

Why not keep it simple, there's no need to try and demonstrate how complicated one can make it look. - but they get off on it, makes them feel superior.

I've often looked at many concepts from maths students on the web, and the most simple equations are deliberately turned into cryptic crosswords, kind of like some secret nerds club ;)

[jfc]

Crash,

Let me try to answer your horse question first.

The assumption is that all 10 runners have equal chances.

The chance of your 3 picks filling 1st, 2nd and 3rd in any order is the spreadsheet expression:

=1/combin(10,3)

=1/120


The Peter gamble is actually a variation of the infernal St Petersburg Paradox. I only found out about that today, and I'll comment if I can work my way through it.

[jfc]

Isn't it wonderful how some scientists and mathematicians turn simple theory into blithering shortcuts and Bachelor of Mathematics speak.

Why not keep it simple, there's no need to try and demonstrate how complicated one can make it look. - but they get off on it, makes them feel superior.

I've often looked at many concepts from maths students on the web, and the most simple equations are deliberately turned into cryptic crosswords, kind of like some secret nerds club ;)

Do you have any idea who you're trying to put down?

http://en.wikipedia.org/wiki/Christiaan_Huygens

If you bother googling the news you'll find the Huygens legacy is prominently performing right now.

He discovered that Saturn had rings as opposed to the presumed bulges. Quite impressive considering he had to invent a suitable telescope first.

[whiteycat2005]

JFC.

Ah Ah Ah Ah Ah Ah Ah Ah Ah Ah Ah Ah Ah Ah nearly there, keep at it mate I'm sure you'll get there.

[jfc]

...
Peter's gamble
Peter asks me for a bid on the following gamble. I get to
flip a coin up to 10
times. If I get heads on the kth
flip, 1 . k . 10, I collect 2k1 and stop. If I
manage to
flip tails 10 times in a row, I collect 1024.
How much should I offer Peter for this gamble? In theory, the value of
this gamble is
· 210
(1=2 · 1 + 1=4 · 2 + 1=8 · 4 + :::+ 1=210 · 29) + 1=210
= 10 · 1=2 + 1
=6.


The Peter's Gamble example should make sense if you try to work through it with a spreadsheet.

The amazing thing to me, is that it illustrates Huygens propensity for inventing incredibly useful things.

After he invented Expectation he then had to prove it. So to do that he invented Hedging! I'd always thought that Hedging was a modern concept.

The example illustrates Hedging as a proof of Expectation.

It shows how you can convert an Expectation of 6, with huge volatility into a guaranteed return of 6. By using appropriate hedge bets.

Right now there appear to be around 10 documented investor/gamblers each heading towards a billion from scratch. In no small part thanks to Huygens.

[Chrome Prince]

Do you have any idea who you're trying to put down?



Yes, I'm not putting down the mathematicians or scientists, I'm putting down the use of superfluous explanations of simple facts - it's simply to make them feel superior.

The courts and police do exactly the same thing trying to stamp superiority - unfortunately it doesn't work!

I read overcomplicated formulae and soon realize that these people are not as intelligent as they try to make out, if they were, they would make things easier for themselves and stop wasting time trying to fluff their own feathers.

[Chuck]

not sure if this has been done before, but anyway i love this little scenario

you are in a gameshow where you are shown 3 doors. you can't see whats behind them. the host says to you that behind each of the doors there is either a car or a goat. of the 3 doors there are 2 goats and 1 car. Obviously you want to pick a car. So you pick a door (for arguments sake door 1). The host opens a different door (e.g. door 2) and there is a goat behind it. He asks you do you want to change doors.

Do you, or does it not matter in your quest for the car?

mathematically you should change doors, although prima facie it is 50/50

[KennyVictor]

OK I'll ask, why should we change doors?

[jfc]

not sure if this has been done before, but anyway i love this little scenario

you are in a gameshow where you are shown 3 doors. you can't see whats behind them. the host says to you that behind each of the doors there is either a car or a goat. of the 3 doors there are 2 goats and 1 car. Obviously you want to pick a car. So you pick a door (for arguments sake door 1). The host opens a different door (e.g. door 2) and there is a goat behind it. He asks you do you want to change doors.

Do you, or does it not matter in your quest for the car?

mathematically you should change doors, although prima facie it is 50/50

This is the notorious Monty Hall Problem.

It is dealt with comprehensively in this 520 page book.

http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf

As are:

Woof's earlier controversy - BG,BB,GB

The St Petersburg Paradox

Markov Chains

Expectation


It is a remarkably readable accumulation of profound wisdom.

For CP's benefit it ain't something to speed read through.

[Chuck]

OK I'll ask, why should we change doors?

The chance of winning the car is doubled when the player switches to another door rather sticking with the original choice. The reason for this is that to win the car by sticking with the original choice the player must choose the door with the car first, and the probability of initially choosing the car is 1/3. Whereas, to win the car by switching the player must originally choose a door with a goat first, and the probability of choosing a goat door first is two in three.

At the point the player is asked whether to switch there are three possible situations corresponding to the player's initial choice, each with equal probability (1/3):

The player originally picked the door hiding goat number 1. The game host has shown the other goat.
The player originally picked the door hiding goat number 2. The game host has shown the other goat.
The player originally picked the door hiding the car. The game host has shown either of the two goats.
If the player chooses to switch, the car is won in the first two cases. A player choosing to stay with the initial choice wins in only the third case. Since in two out of three equally likely cases switching wins, the odds of winning by switching are 2/3. In other words, a player who has a policy of always switching will win the car on average two times out of the three.


Lovely

[crash]

Chuck,

A smart presenter [Bob Dyer of 'pick-a-box' fame ....yes I'm that old] would of course know that theory and for obviously smart contestants like Barry Jones [was the all time pick-a-box King], Bob would use reverse psychology and offer the door with the car, not the goat. Barry Jones would counter with reverse, reverse psychology of course and take it :-))