ROR calculations for HU with Martingale betting

[dwr]

A friend is playing HU to accumulate a bigger bankroll and is playing under the following rules.

He plays the $10,$20,$50,$100 and $200 levels. All levels have a 5% fee.

Each session he starts at the $10 level. He stops a session if he wins +$100, or loses -$500 (or the next buy-in takes him over that stop-loss)

If he wins a match, he then moves to the $10 level.

If he loses a match, he moves up a level.

He starts with a bankroll of $2000.


How do I begin to calculate a risk of ruin with this sort of martingale in the middle?

What is the minimum probability of winning matches that produces a ROR of less than 1%?

And how would I incorporate a changing probabilty of winning for the different levels (oddly enough he actually has a better return at the 2nd and 3rd level than the 1st.)?

Is the maths really as complicated as I'm finding it?

I have searched for ROR calcualtors etc but they don't seem applicable.


Any help is appreciated.

[pococurante]

Let's say your friend is good enough to win 50% of his games (though it's unlikely, if he thinks martingaling is a good plan).

Every time he loses 5 games in a row, it's a $400 loss (at which point he stops). All other results are a $10 profit.

Odds of losing 5 in a row: 1/32.

So he will win $310 for every $400 lost.

Add in the likelihood he will tilt or continue to play for larger amounts after running into a big loss, and the ROR is just about 100%.

There is absolutely no intelligent reason to play like this, instead of grinding out lots of SNGs at the same buyin level.

IMO, poker would be so much easier if the software had an option where you could force it to restrict you to only $10 buyin games for the next 2 weeks, or something like that.