You're missing the obvious way to exploit this: all consumers stand to benefit a maximum of two cents from each purchase they make by carrying both cash AND car

You're missing the obvious way to exploit this: all consumers stand to benefit a maximum of two cents from each purchase they make by carrying both cash AND card. Since rounding only happens when paying cash, simply pay cash if the purchase could be rounded down ($_._1 or $_._2), and pay card if it could rounded up ($_._3 and $_._4). In practice, no one gives a shit because it's a penny and no one cares about the penny. QED