The math works the same as with any other investment on earth.
Bankroll:
You own 1 BTC. BR is 2 BTC. It doubles. You own 2/4 BTC or 50% still. You cash out earnings, you now own 25%.
Walmart, MCD, (insert company here):
You own 2 shares out of 4. Shares are worth $0.50. Shares double in price. You cash out profit. You now own 25% (as you sold 1/2 of your shares out of 4 and now own 1/4).
This is all basic economics.
Damn lad, you just explained every investment in just 2 sentences, you must be some sort of genius.
Now go on and do the same for non-publicly trading startup, for investing in gold bullion, bonds, investing in art, collectibles, cars, personal education, or...bitcoin. Any investment on earth, right?
Also, you could invest in dividend paying shares and cash them out without affecting your holding and with no need of re-investing. Still the same as investing in BR? Why would you equal profit on players' losses with the value of listed company, rather than its profits?
Also 2, increase in stock price (apart from clear speculation) is a result (or expectation) of growth in sales, or just higher profitability. Smaller slice of bigger cake. Not really the case for investing in bankroll is it?
Gold, art, collectibles are all stores of wealth. Cars can either be a store of wealth or a depreciating asset, depending on what you're purchasing. Education isn't an investment in the traditional sense. Bitcoin is treated like gold (store of wealth). You do not invest in a store of wealth, you purchase it. You can invest in companies that back them, but that's an entirely separate story. Bonds are generally not seen as investments, either. That'd be like saying a savings account is an investment -- it's not, it's a generally secure store of wealth that can be reasonably expected to curb inflation by a small percentage.
Stocks that give dividends have their prices lowered by the dividend amount once it's announced. If the stock were $1 and is paying out a $0.10 dividend, its price would be naturally lowered to $0.90 to resume the same pricing as before. The vast majority of investors DRIP, so if you're not, it's the same as just selling off x number of a stock that doesn't pay dividends.
I'm not going to sit here explaining basics to you. I have work to do.