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Let's call your roll 30. you decide to play 1 dollar SNGs. You have a really nice 20% ROI so you're making twenty cents per. To move up to the $3 level, you want to have $100 to give you 30 BIs or so. So you need to earn $70. 70/.2 = 350 SNGs you have to play assuming you run at 20% plus, which you may not, so it could be more like 500-600. I don't know how much you play a day/# of tables, but for many part timers that is a huge amount of time.
I am sure if you can beat the $1s for 20% you can beat the $3s for a least 10% (and probably the two will be closer) and that means you increase your ave win from .2 to .3, which is 50%.
So you can either play 500-600 SNGs, or deposit ~100 bucks. You'll learn a lot playing the 500-600 so there is nothing wrong with it. But in addition to moving up quicker with the despoit, you could use the "time saved" to study rather than grinding the last xx tourneys.
If you were going to deposit 5k to play $100 SNGs, I'd say make it 1k and grind through lower BIs first. But the same logic doesn't apply < $10-20 or so (imo) because you'll have new players all through those limits, as well as many recreational players who are never going to be any good but can afford to donk off $500 a month.
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