By analyzing 30 min, high-resolution recordings of single Escherichia coli flagellar motors in the physiological regime, we show that two main properties of motor switching-the mean clockwise and mean counter-clockwise interval durations-vary significantly. When we represent these quantities on a two-dimensional plot for several cells, the data do not fall on a one-dimensional curve, as expected with a single control parameter, but instead spread in two dimensions, pointing to motor individuality. The largest variations are in the mean counter-clockwise interval, and are attributable to variations in the concentration of the internal signaling molecule CheY-P. In contrast, variations in the mean clockwise interval are interpreted in terms of motor individuality. We argue that the sensitivity of the mean counter-clockwise interval to fluctuations in CheY-P is consistent with an optimal strategy of run and tumble. The concomittent variability in mean run length may allow populations of cells to better survive in rapidly changing environments by 'hedging their bets'.