Specifically, a scenario is presented where miners could choose between normal mining, which yields fees from two blocks as $a$ and $b$, and strategic mining, which alters the fee extraction to $a_1$ and $b_1$ with $a_1 < a$ but $a_1 + b_1 > a+b$. This strategic adjustment implies that while the immediate return from the first block ($a_1$) under strategic mining is lower than that of normal mining ($a$), the combined return from both blocks under strategic mining surpasses the total fees extracted through normal mining.

The payoff matrix further elucidates this strategy by detailing the probable outcomes based on the proportion of hash rate ($h$) dedicated to strategic mining versus normal mining. It outlines four scenarios: both blocks mined strategically, one block mined normally and the other strategically in both possible orders, and both blocks mined normally. For strategic miners, the expected payoff is calculated as $h ( a_1 + h\cdot b_1 + (1-h)b )$, signifying that their total expected returns depend on their hash rate's proportion engaging in strategic mining. Conversely, the expected payoff for normal miners is given by $(1-h) ( a + h\cdot b_1 + (1-h) b )$, highlighting that their returns are inversely related to the hash rate committed to strategic mining.

Analyzing these payoffs reveals an intriguing insight: when adjusting for their respective hash power, the proportional payoff for normal miners actually proves to be higher since $a > a_1$. This outcome suggests that despite the seemingly advantageous position of strategic miners in terms of total fee extraction, normal miners, when accounting for their hash power investment, may find themselves benefiting more on a proportional basis. This nuanced understanding of mining strategies underscores the complex economic and strategic considerations at play within cryptocurrency mining operations, emphasizing how different approaches to block mining can yield distinct advantages depending on the broader context of miners' hash rate distribution and strategic choices.