How tenuous is the Democratic advantage in the Senate

16 states currently have a partisan split between the Governor and the Senators. Of these 16 states, 9 allow the Governor to appoint a replacement from a different party until the expiry of the original term, or the next statewide election: Georgia, Kansas, Kentucky, Pennsylvania, Maine, New Hampshire, Montana, Ohio, and West Virginia. A further three also allow gubernatorial appointments from a different party, but with a proximate special election to be held: Louisiana, Massachusetts, and Vermont.

7 of those states have Republican governors and Democratic senators and 2 have Democratic governors and Republican senators, meaning there are many more opportunities for Republicans to flip the Senate with an opportune death than there are for Democrats. And more so since the Democrats are older. The Democratic Senators by state and age are:

And the Republican are

Using the Social Security actuarial life table and the some high school math, it turns out that, when Congress started, there was a 49.44% chance that one of these critical Democratic Senators would die before 2023. There's only a 12.55% chance that one of the Republicans will. [Note: US Senators are likely of better health, and definitely have access to better care, than the average American their age does and so these numbers are likely inflated.] That means there was 43.23% chance that at least one of the Democrats would die and none of the Republicans would and the Senate would flip (This ignores the rare situations in which two Democrats die and only one of these Republicans, or three and two or five and four, etc...).

With each day that probability goes down. At the start of 2022, the probabilities will be 29.56%, 6.72% and 27.57% and then continue to drop. [Update: While true at the beginning of 2022, it quickly got worse when Republican Glenn Youngkin flipped the Virginia Governor's mansion creating two more at risk Democratic seats. Tim Kaine is 64 and Mark Warner is 67.]

Nonetheless, every day the Democrats don't pass the legislation they want to pass they're rolling the dice and the dice are not in their favor. RBG gambled too when she didn't resign while Democrats controlled the Senate and liberals lost when she did.