"I wonder if you can still achieve results with small amounts...

"I wonder if you can still achieve results with small amounts like 20k or lower."

Your return will be the same if you own one share, or one million shares, so having only a few grand to invest doesn't preclude you from achieving good investment returns. However, the more you have to invest, the less that brokerage will cost you in percentage terms.

For example, if your broker charges $20 per trade, and you invest $1,000 in a company, then by the time you sell the shares, you need them to have become 4% more valuable just to recoup your brokerage. If you have $10,000 to invest, then you only need the share price to rise by 0.4% to break even. With $3,000 I'd suggest that you pick one LIC, remembering that each LIC is very much diversified already. Whether you pick ARG, MLT, CHO or one of the others probably won't make a huge difference. After all, if I knew which of the LICs will be the best performer over the next few years, I'll put all my money in that LIC and not bother with any of the others.