Can we model risk with only probability?
I don't think it even makes sense to talk about risk without specifying the payoffs.
Take your two examplary gambles and suppose that $a=b=c=d=e=0$. In that case, there is no risk involved at all. It is like flipping a coin and if it lands Heads, nothing happens, and if it lands Tails, nothing happens. This would not even be considered a gamble.
Alternatively, let $a=b=c=d=0$ and let $e&gt;0$. Then gamble $B$ gives you the possibility of free money. Similarly, let $a=b=c=d=0$ and let $e&lt;0$. Then gamble $B$ simply is a possibility to burn money with some probability. However, these two gambles $B$ are very different.
Alternatively, suppose that all $a,b,c,d,e$ are events. The first four are associated with some payoff and in event $e$ simply gamble $A$ is played. Then gamble $A$ is in fact gamble $B$. Without a specification of the events, you cannot compare the two.