This is something of an understatement. If the Yellowstone
Supervolcano actually
erupts, not has a channel open, not has a lava tube open, but full-up
erupts.
Here's a link to the deadliest-known Volcanic eruption
Mount Tambora in 1815, which killed a minimum of 70,000 people, probably more than a 100,000,
directly.
Indirectly it caused the worst famine of the 19th century, and 1816 was known as 'The year without a Summer' as a consequence.
Mount Tambora was an eruption with a Volcanic Eruption Index (VEI) of 7. The scale is logarithmic, so each step is 10x as strong as the level below it. For comparison, Vesuvius and Mount Saint Helens were VEI
5, so around a
hundredth the size of the Tambora eruption.
Two of the known major eruptions from the Yellowstone Supervolcano, were VEI
8, literally the highest category that Vulcanologists track. To be clear, those were two separate eruptions from the 4 different
major caldera of Yellowstone.
A VEI 8 eruption would kill everyone in Yellowstone more or less instantly, most of Wyoming, Yellowstone, and Idaho would probably be rendered uninhabitable, with pumice (hot stone) falls probably killing thousands, and ash burying entire towns as people evacuate.
The ash in the atmosphere would almost certainly cause a famine across the entire northern hemisphere, and depending on the force and direction, it might get into the southern hemisphere too. The famine in the northern hemisphere could last
years.
If
all four caldera erupt at once?
That's a literal act of god, obliterating most of North America, and possibly scaling up to a near-extinction event.
Now, most likely by far, we'll just see a continued simmering. The constant simmering makes even minor eruptions less likely, and full eruptions very improbable.
