E = Dr x Pw – R x Pl
 

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 ….......

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/...ens/huygens.pdf

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

http://www.math.dartmouth.edu/~doyl...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.

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

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 :-))

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.

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 ;)

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.

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.

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.