In the Rule entitled “Duels”, change the text

The winner of a Duel adds an amount of Cookies equal to twice the amount that was bet.

to

The winner of a Duel adds an amount of Cookies equal to twice the amount that was bet.  Also, both the winner and the loser of the Duel receive an amount of Cookies equal to one-third of the total Heartbeat lost during the Duel, rounded down.

We can think of this as Cookies skimmed from legal bets placed by non-Breeders, but the real point is to let both sides recoup some of their lost Heartbeat, making battling slightly less risky.