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.