I have studied the Kelly criterion in relation to bet-sizing based on positive expected value (EV) events. However, I can't figure out a way to adapt it to solve the following problem:
Let's say we have event $A$ paying $5$ decimal odds, i.e., bet $\$1$, receive $\$5$ back (profit $\$4$), but we know the probability of the event occurring is $> 0.2$.
That is the only information we have. We know the event is positive EV, the extent to which is unknown. To reduce variance, betting less on lower-probability/higher-odd events seems to be a goal.
Do any bet-sizing strategies exist to fit this information? I've considered simply linearly/exponentially reducing bet-size as a function of higher decimal odds.
You cannot really answer this question completely, I think, without having some idea (like a prior probability distribution) of how the win probability $p=\frac{1}{5}+\alpha$ is distributed for $\alpha \in (0,4/5].$
Armed with this information you could apply an optimization, by maximizing an appropriate criterion, possibly subject to some constraints.
Edit: In response to your comment, use the approximate value of $\alpha$ to compute $p$ or if you have distributional information compute $Q(p)$ the probability distribution of $p.$ Let $\overline{p}$ be the mean computed from $Q(p)$ or the approximate $p.$ Then one approach would be to bet the fraction given by Kelly criterion thus: $$ f^{\ast}=\overline{p}-\frac{1-\overline{p}}{b} $$ with $b=4,$ the proportion of net win to amount wagered. To be more aggressive I suppose you could use $\overline{p}$ to be the say $q-$th quantile instead of the mean with $q=0.6,$ for example. Or since the median is a bit less sensitive to noisy information take $\overline{p}$ to be the median instead of the mean.