Okay, so I rewrote the script and it now behaves normally.

I made a first bunch of calculations in the train.

The BRM chosen is simple:

br = starting bankroll

brm = we play a game at the highest stake possible for which we have "bankroll > brm*stake"

$ = average bankroll at the end of 5k games following the BRM

brokes = percentage of brokes.

average of 2k runs of 5k games, better edge=60% itm:

br: 50 brm: 1000 $: 323 SD: 59 $, brokes: 0.0 %

br: 50 brm: 500 $: 323 SD: 18 $, brokes: 0.0 %

br: 50 brm: 200 $: 447 SD: 96 $, brokes: 0.0 %

br: 50 brm: 150 $: 602 SD: 168 $, brokes: 0.0 %

br: 50 brm: 100 $: 1815 SD: 1120 $, brokes: 0.0 %

br: 50 brm: 75 $: 6594 SD: 85 $, brokes: 0.0 %

br: 50 brm: 62 $: 16793 SD: 19783 $, brokes: 0.0 %

br: 50 brm: 50 $: 35178 SD: 17608 $, brokes: 0.0 %

br: 50 brm: 30 $: 66723 SD: 12418 $, brokes: 0.0 %

br: 50 brm: 10 $: 95583 SD: 11467 $, brokes: 0. %

br: 50 brm: 5 $: 92607 SD: 20175 $, brokes: 0.73 %

br: 50 brm: 3 $: 42032 SD: 71514 $, brokes: 8.57 %

br: 50 brm: 2 $: 16039 SD: 96027 $, brokes: 14.92 %

So far, a few things, quite logical can be taken out of this:

-> a too nit BRM will slow down our progression.

-> a too aggressive BRM will also slow down our progression. The average takes into account the "0$" out of the brokes, and therefore shows that too aggressive doesn't mean better.

-> for a player with 60% itm and 6.6% rake on his network, a BRM of 10BI seems around optimal. It seems quite logic to have an aggressive BRM as optimal for a stake we already beat.

Next will come calculations in "one stake" only, just to try to correlate our expected ROI with an optimal BRM to start a new stake.

After this, it will be quite easy to guess something close to optimal BRM for moving up stakes as fast and secure as possible, if able to estimate our ROI at the next stake.

And finally, I'll compare these "optimal BRM" found to BRM commonly used.

That's gonna be a bit of work though, so of course I don't know how long it'll take

My first calculations were done with 54% ITM. Actually with the standard deviation displayed I understood why the first results were strange: the standard deviation was about the same as the "end" bankroll", meaning we had a value totally unexploitable. That's why I decided to get the ITM up.

ROI should decrease at higher limits. Reason: Reflects real world.

If possible, calculate winrates in BB/100 using typical winrates from the various levels. Reason: Results more easily understood

When BR < X BI, start decreasing winrate, and decrease it geometrically as BR decreases. Reason: Adjusts for "scared money" and reflects how people tend to behave when on a downswing.

I agree with the first point. However I was aiming at first looking if BRM had a significant impact or not, so a constant ROI was necessary imo.

Calculating the bb/100 has no use imo to a SnG HU player. I'll later on maybe translate this tool for cash game, but that's not my idea since I don't play CG anymore.

As for the third point, it would be quite easy to do so, but I'm not interested in. I'd argue that it this should already be comprised in the itm% chosen. Also, our ROI is a estimation, and therefore it doesn't make sense to add such thin details on something that is already not precise at all.

I mean, if we know for sure our winrate over more than 1k games at a stake, I'm not really sure that an estimating tool for BRM is needed to chose a BRM.

However of course these things can be implemented in