Blackjack’s signal-to-noise ratio

I just read that (mean/s.d.)² is one definition of signal-to-noise ratio, another interpretation of DI² or c-SCORE. (Replace mean with win rate.) Win rate is the “signal” and the rest of the curve is “noise.” Higher DI² = clearer wins, less obscured by variance, less risk.

Relative standard deviation

When comparing standard deviations, converting absolute to relative s.d. by dividing by the mean gives an apples-to-apples comparison of the widths of the distribution curves. Such as when comparing bet ramps with and without splitting to two hands, or risk-averse indices. The inverse is the Desirability Index; but since DI² has become the de facto means of comparing two games, why not replace the unsquared DI with its inverse, r.s.d., for an intuitive evaluation of the curves.
Example: win rate 2.3 units, s.d. 53 units, vs. win rate $60, s.d. $1125. Relative s.d.’s are 23.04 and 18.75, reflecting the narrower curve and reduced variance of the second game. DI²’s are 18.83 and 28.44, reflecting more money to be won with less risk by the latter.

Relative variance

DI² = win rate when risk of ruin is about 13.5% (a premise of the original SCORE). When win rate is greater than DI², risk is high, and vice versa. The ratio of win rate to DI² is equivalent to relative variance, (s.d.)²/win rate, and varies directly (but not linearly) with risk of ruin, independent of bankroll or other factors, and can be used as a proxy. A r.v. of 0.67 corresponds to RoR of 5%, and 0.43 to 1%. Maybe a little more useful than the CE/win rate ratio.

r.v. RoR
0.43 1%
0.51 2%
0.57 3%
0.62 4%
0.67 5%
0.71 6%
0.75 7%
0.79 8%
0.83 9%
0.87 10%
0.91 11%
0.94 12%
0.98 13%

fwiw.