I would look at it from an expected return perspective. Play around with the numbers below based on your knowledge of the company. I plugged in some values and came up with an expected return of $4,200. Those numbers are completely made up but you can see the concept.
What are the odds that it becomes entirely worthless? 25%?
What are the odds you basically break even? 50%?
What are the odds it doubles? 20%
What are the odds it goes up 10x? 5%?
$3,000 X .25 X 0 = $0
$3,000 X .50 X 1 = $1,500
$3,000 X .20 X 2 = $1,200
$3,000 X .05 X 10 = $1,500
Expected return = $4,200
If $3,000 is not a significant part of your net worth/liquid cash I would go for it. The downside is $3,000 loss but the upside could be buying shares at $2.00 that you could potentially sell for $4, $5, $10.