THE TURF. 
to have made better bets for instance, could he 
have done better than by taking an even three pounds 
on the first event, and had greater odds than 6 to 4 
on the latter, he might have won, but could not have 
lost. 
On the same two events, what odds may B lay A 
that the latter does not lose both ? Set down for the 
former -J, and the latter will now be T 4 ^ ; but T \ is 
equal to j- ; therefore, it will be 
1 2 2 
2 ><-=-; and 10-2=8: 
hence the odds are 8 to 2 = 4 to 1. 
Proof by Hedging. B begins to hedge by betting 
an even one pound on the first event, which, A winning, 
he wins. On the subsequent event, B takes the odds, 
3 to 2, which, A winning, he also wins. Thus he 
receives four pounds, which pays the 4 to 1 he betted 
on A losing both events. 
Upon two several events, even betting on the one, 
and 7 to 4 in favour of A on the other ; what odds may 
B lay against A winning both ? The one, as before, is 
J, and the other is represented by -j^ : 
thus 15 to 7 is the odds. 
Proof by Hedging. The sum against which B laid 
his odds is 7; therefore he begins by laying seven 
pounds on the first event ; which, as A wins, he wins. 
255 
