Based on the official numbers for England, the chances of catching the Delta variant are 1.55% if you're unvaccinated and 0.42% if you're vaccinated, meaning that unvaccinated people are 3.7 times more likely to catch Delta. However, the chances of DYING of the Delta variant once you've caught it are 0.28% if you're unvaccinated and 1.02% if you're vaccinated, meaning that you're 3.6 times more likely to die from Delta if you're vaccinated.
Therefore, the overall chances of anyone in England dying from the Delta variant are 0.0044% for unvaccinated and 0.0043% for vaccinated. So, being vaccinated seems to increase the average person's chances of survival by just 0.0001%.