Bankroll limited house edge

I was playing blackjack the other day, and the person playing next to me bought in for only 4 units, then proceeded to bet 1 unit, win, then bet 3 units loose, and then bet his remaining 2 units and loose. This small buy in and aggressive betting clearly is not optimal because the player doesn't always have enough money 'behind' to properly split and double. This led me to wonder what the house edge is if you only have n-units on the table and can't (or won't) get more. Clearly if you have only 1 unit and bet it, thats the same as playing a game that doesn't allow doubles and splits. According to Blackjack Bluebook II, doubling and splitting is with 2% of your wager, and is a significant thing to give up! If you have 2 units, you will be able to double or split once, and that will cover many cases, but there will still be times when you can't double after split or resplit. We know that DAS and resplitting combined is worth about 0.2%, so that's not so bad. If you have 3 units, you will not be able to handle the rare double after resplitting and such, but that is worth something.
Does anyone know of a table that shows the house edge for 1 , 2, 3, 4,5, ... units behind? If I am having a losing session, do I stop when I have two units left? 3? (I am assuming a basic strategy player flat betting)

This may have been addressed before, but I could not find it. It is tricky to come up with the right search terms too! I thought I might find a discussion somewhere about "bold play" in blackjack, but I could not.

Interesting question. I've never seen someone not reach into their wallet or purse for more if they need to double or split. It's kind of funny to watch, as they always look really embarrassed. The one or two times they didn't come up with the extra money, I offer to put it up for them if it's a 9, 10 or 11 against a dealer upcard of 3-6, or an offensive split that isn't 9-9. Be sure to clarify that it's "your bet," and not a short-term loan. Of course you have a significant edge on those bets.

I saw a guy buy in for $400 and bet one black at a time. Some people get a rush out of "playing short." If I recall he did pretty well -- never got down to his last chip. The disadvantage to not doubling or splitting would vary as to what double or split was (e.g. 8-8 v. A or 11 v 6), but in the long-term it wouldn't have much effect if you didn't encounter the situation often.

I think what you are referring to is Gambler's Ruin.... the potential for going flat broke during a session of normal variance. The Avoidance of Gamblers Ruin is usually presented at the 90 percent level and is related to Time At Table using perfect Basic Strategy.

In order to play ONE HOUR at blackjack using absolutely perfect Basic Strategy and not tipping dealer or waitress playing only one hand and making no mistakes, you must start with 19 units and will have only a ten-percent likelihood of hitting the felt before the one hour is up. Any tipping, any mistakes, any multiple hands, any dealer errors .. and you need even more than 19 units.

Now some people may buy in "short" because it imposes a limit on them. If there luck is 'bad' they simply accept that fact and move on. I've also seen people buy in for a small fortune at the craps table and then bet only Reds the whole day. Annoys the hell out of the dealers I'm sure.

Quote: FleaStiff

I've also seen people buy in for a small fortune at the craps table and then bet only Reds the whole day. Annoys the hell out of the dealers I'm sure.

Why would that annoy the dealers?