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In the literature, there are various notions of stochasticity which measurehow well an algorithmically random set satisfies the law of large numbers. Suchnotions can be categorized by disorder and adaptability: adaptive strategiesmay use information observed about the set when deciding how to act, anddisorderly strategies may act out of order. In the disorderly setting, adaptivestrategies are more powerful than non-adaptive ones. In the adaptive setting,Merkle et al. showed that disorderly strategies are more powerful than orderlyones. This leaves open the question of how disorderly, non-adaptive strategiescompare to orderly, adaptive strategies, as well as how both relate to orderly,non-adaptive strategies. In this paper, we show that orderly, adaptivestrategies and disorderly, non-adaptive strategies are both strictly morepowerful than orderly, non-adaptive strategies. Using the techniques developedto prove this, we also make progress towards the former open question byintroducing a notion of orderly, ``weakly adaptable'' strategies which we proveis incomparable with disorderly, non-adaptive strategies.

Comparing disorder and adaptability in stochasticity