Sequences of repeated gambles provide an experimental tool to characterize
the risk preferences of humans or artificial decision-making agents. The
difficulty of this inference depends on factors including the details of the
gambles offered and the number of iterations of the game played. In this paper
we explore in detail the practical challenges of inferring risk preferences
from the observed choices of artificial agents who are presented with finite
sequences of repeated gambles. We are motivated by the fact that the strategy
to maximize long-run wealth for sequences of repeated additive gambles (where
gains and losses are independent of current wealth) is different to the
strategy for repeated multiplicative gambles (where gains and losses are
proportional to current wealth.) Accurate measurement of risk preferences would
be needed to tell whether an agent is employing the optimal strategy or not. To
generalize the types of gambles our agents face we use the Yeo-Johnson
transformation, a tool borrowed from feature engineering for time series
analysis, to construct a family of gambles that interpolates smoothly between
the additive and multiplicative cases. We then analyze the optimal strategy for
this family, both analytically and numerically. We find that it becomes
increasingly difficult to distinguish the risk preferences of agents as their
wealth increases. This is because agents with different risk preferences
eventually make the same decisions for sufficiently high wealth. We believe
that these findings are informative for the effective design of experiments to
measure risk preferences in humans