Plausibly, there is a strong correlation between good deeds and salvation. Both are the fruit of God's grace. If evidential decision theory is correct, then the fact that good deeds correlate with salvation makes it rational to do good deeds. Thus, if evidential decision theory is correct, then it makes rational sense to do good deeds for self-interested reasons, even if the good deeds in no way causally contribute to salvation.
What conclusions could be drawn from this? Well, this means that even if sola fide were true, and good deeds in no way contributed to salvation, nonetheless it would be self-interestedly rational to do good deeds for the sake of salvation. This in turn means that those Protestants whose motivation for embracing sola fide is that the doctrine makes it not make sense to do good deeds for the sake of salvation either need to reject either evidential decision theory or their motivation for sola fide. Or one might draw a more ecumenical conclusion. If we all accept evidential decision theory, then our stance on the metaphysical question of sola fide need not affect our practices and motivations: Lutherans, Calvinists, Catholics and Pelagians can all consistently do good deeds for the sake of salvation.
The above argument would be particularly interesting if it turned out that causal decision theory requires indeterminism. For the above argument might give my Calvinist friends reason to reject evidential decision theory, and hence to embrace causal decision theory, and hence to reject determinism. (A Calvinist does not need to be a determinist. She could embrace the position that W. Grant Matthews attributes to Aquinas in a fairly recent issue of Faith and Philosophy.)