However, now with the reverse split you now only have
1000 shares. The stock still opens at $20 and still
closes at $60.
That's off. Why are you assuming people would pay the same amount for 8 times as much of the company, instead of 8x more? A better guess would be that if before it would have gone $20 -> $60, then after a 8 -> 1 reverse split it would have gone $160 -> $480.
The only reason splits exist is that people have an irrational attachment to the value of a "share" and expect to see it in a certain range, even though the total number of shares available is a number chosen more or less arbitrarily by the company.
The only reason splits exist is that people have an irrational attachment to the value of a "share" and expect to see it in a certain range, even though the total number of shares available is a number chosen more or less arbitrarily by the company.