allowing your opponent to martingale you

[lgas]

I found myself in a situation the other day where I was playing against an opponent who was not horrible but whom I outclassed pretty significantly. We played a series of heads-up freeze outs. We played for $40 and I won, rematch for $40 and I won, another $40 and I won, $100 and I won, another $100 and I won, so at this point I am up $320 and have won 5 in a row. He now wants me to offer him 200 to 180 odds (so if he loses, he'll owe me an even $500 but if he wins, he'll only owe me $120). I decided that I thought I was easily enough of a favorite to offer these odds and did so. I lost and we quit (he had an appointment to get to or I'm sure we would've played more).

Thinking about it later I realized that I essentially was letting him try a martingale-ish/double-or-nothing-ish stragety against me. Of course it wasn't quite a martingale as the bets didn't actually double each time, but it was similar. If he didn't have to leave and I had won the last freeze-out, he could have then offered to play for $300 or $400, which, while not strictly a martingale, would get his debt back into very small numbers if he won -- if he lost this, he could've offered to play for $550 or $700 or whatever, etc.

So my one thought is that the general thinking seems to be that if the game is good you should keep playing. In this case, I know the game is good and I have a rather significant advantage over my opponent and I am a big favorite to win any individual match... but if I keep letting him increase the stakes I'm bound to lose one sooner or later which lets him get even (or close to it). The situation would be even tougher if he was doing an exact martingale ($40 on the first game, $85 on the second game, $175 on the third game, etc or something like that).

Obviously I have the opportunity to refuse to play each subsequent game, so I could've for example stopped after I was ahead $320. This seems to be my only advantage in this scenario.

So I guess my questions are:
1. How many times should you (as the favorite) accept rematches against an inferior player using a martingalish strategy against you... Obviously this is dependent on exaclty how big a favorite you think you are... I'd say I was probably at least a 60/40 favorite and maybe as high as a 75/25 favorite against this particular player... feel free to use other numbers though if it makes the example easier/clearer.

2. Is there a better way to handle this type of situation? Like accept N rematches while allowing the stakes to double then only agreeing to rematches for the same amount (say $100) from there on out?

3. Obviously the big drawback to the martingale strategy in general is that if you hit a particularly bad stretch your losses can grow really high really fast. Assuming that you are playing on a cash basis, extending no credit, what size backroll does your inferior opponent have to have before you are willing to risk allowing him a martingale every time in hopes of busting him completely?

In our specific situation, my opponent is significantly wealthier than I am and could probably afford to keep doubling to somewhere in the $20k-$30k range before it would get too painful for him to keep playing... if we had started at $40 and done strictly double or nothing this would be a 40-80-120-240-480-960-1920-3840-7680-15360 progression, or in other words I would have to win 10 times in a row before I shut him out (which would've booked me a nice $30,720 win).

4. What other things should I be considering in this situation? What type of arrangement can I propose that gives me the best odds of extracting the most money from him?

Thanks in advance for any input,
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John