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Just to add- the higher the stakes you're playing, the higher the variance, since people play trickier and more aggressively. Consequently you want more buy-ins if you're playing higher stakes. Also at the lowest stakes the variance is going to be high, due to people playing poorly, so you want more buy-ins compared to middle stakes.
Here's my completely arbitrary guideline for how big a bankroll you need to grind comfortably at a certain stake.
.5/1 4,000 (40 buyins)
1/2 8,000 (40 buyins)
2/4 14,000 (35 buyins)
3/6 21,000 (35 buyins)
5/10 40,000 (40 buyins)
10/20 100,000 (50 buyins)
25/50 250,000 (50 buyins)
50/100 500,000 (50 buyins)
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