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Layer 2 rollups are rapidly absorbing DeFi activity, securing over $40 billion and accounting for nearly half of Ethereum’s DEX volume by Q1 2025, yet their MEV dynamics remain understudied. We address this gap by defining and quantifying optimistic MEV, a form of speculative, on-chain MEV whose detection and execution logic reside largely on-chain in smart contracts. As a result of their speculative nature and lack of off-chain opportunity verification, optimistic MEV transactions frequently decide not to execute any trades. In this work, we focus on cyclic arbitrage, which we find is predominantly executed as optimistic MEV on Layer 2s. Using our multi-stage identification pipeline on Arbitrum, Base, and Optimism, we show that in Q1 2025, transactions from cyclic arbitrage contracts account for over 50% of on-chain gas on Base and Optimism and 7% on Arbitrum, driven mainly by "interaction" probes (on-chain computations searching for arbitrage). This speculative probing indicates that cyclic arbitrage on Layer 2s is predominantly executed as optimistic MEV and contributes to generally keeping blocks on Base and Optimism persistently full. Despite consuming over half of on-chain gas, these optimistic MEV transactions pay less than one quarter of total gas fees. Cross-network comparison reveals divergent success rates, differing patterns of code reuse, and sensitivity to varying sequencer ordering and block production times. Finally, OLS regressions link optimistic MEV trade count to ETH volatility, retail trading activity, and DEX aggregator usage. Together, these findings show that optimistic MEV has become a major source of persistent spam-like transaction activity on Layer 2s, dominating blockspace with low-value probes and reshaping the composition of on-chain activity.