If a rational person was given this choice 100 times it would be rational to always chose 10% chance of $1 million, but is having 10k cash in your pocket 10 times as valuable as having 1k in your pocket when compared to having 0 in your pocket?

Money has diminishing returns and when you're potentially going to be below water when it comes to mortgage, food, utility, even the occasional vacation for sanity - then a smaller guaranteed sum can be more valuable than a larger expected sum.