So here is a question I seldom see discussed. Suppose a counter is in danger of tapping out his trip bankroll (oh no!). He is down to his last $600 and the count calls for a wager of $300. What fraction of his on hand capital should he bet? If you bet $300, then you risk losing EV if you have to split and double down on each split because you won't have enough money. There are other variations that would require 4x your initial bet, but you get the idea. Why is it such a big deal if you lose EV by not splitting or doubling? Is it really that much of a loss?

In theory, he could bet anywhere from 1/8, 1/6, 1/4, 1/2, or even the full amount of his leftover capital (maybe the count call for a $600 wager). Intuitively, I sense it would be either 1/2 over 1/4 of what he has left. Some of the big teams say the optimal bet is 1/6 of whatever you have on hand. Have you ever seen a mathematical treatment of this question or do you know of any simple math to justify wagering no more than 1/6th on hand capital?

Thanks,
MJ