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Put simply, your 15 buy-in bankroll is there so that you can absorb a downswing like you're describing without going busto. The idea is to ride out the variance (assuming it is variance) and come back to win a few and start growing that BR.
Having a threshold for moving down a level is another part of the picture. Let's use the $11s (10+1) as an example rather than the 5.50s.
If your bankroll is $165 giving you the 15 buyins at $11, you could set a floor of say $110. If you lose five of the $11s in a row, you broke your floor of $110, you drop down to the $5.50s where you would have ~20 buyins. Play the 5.50s, and set a ceiling of something like $220, then you can move back up to the $11s with a nice comfy 20 buyins and a 10 buyin cushion before you hit your floor again.
Once you're winning at the $11s, you could set a ceiling of say 20 buyins at $22, or $440 -- once you hit that mark, move up to the $22s and set a floor of $220.
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