This section compares deterministic and randomized allocation functions within discount models where miner ratios and time-based discount rates affect outcomes. It introduces the immediacy-biased allocation class (ρℓ), which prioritizes near-deadline transactions, and shows how it performs optimally in a “semi-myopic” regime. The analysis establishes upper and lower bounds for both deterministic and randomized cases, demonstrating that simple deterministic strategies can nearly match the efficiency of their randomized counterparts under certain conditions.