This is why gambling is stupid.. Do everyone a favor and invest in yourself - real skills to give back to the world. “can actually make it possible to generate

This is why gambling is stupid.. Do everyone a favor and invest in yourself - real skills to give back to the world. “can actually make it possible to generate positive returns at the portfolio level, even when all of the portfolio’s individual holdings are expected to produce zero, or even negative, returns over time.” -False The illusion comes from the fact that, for small n you can flip heads and tails the same number of times and still have over half the money you started with - whereas with the invest all strategy you would have lost everything. For a fair coin, as n approaches infinity you still win nothing either way though. That graph is completely misleading. We can represent the amount won as the recursive sequence X_(n+1) = X_n + (X_n)/2 def recursive_sequence(n): """ Money won after winning n times in a row""" result = 1 # money we start with rebalance_ratio = .5 for i in range(0,n): result += result*rebalance_ratio return result for i in range(1,10): temp_profit = recursive_sequence(i) net = temp_profit / 2**i # assuming you loose as many times as you won after percent = abs((temp_profit-1))*100 print(f"savings after {i} heads:", recursive_sequence(i), f"\npercent profit: {percent}","\n....money after loosing n times after: ", net, "\n") You can see what this gives for a rebalance ratio of 0.5. Anything more or less just increases or decreases your volatility. “How returns can be created out of thin air” is literally a scam - not true. That’s a tulip bubble. Sure you can get rich off one if you fool enough people. You need to flip a coin 2^(n+1) – 2 times to get heads n times in a row. Same for tails… Your “rebalancing” is only increasing the number of attempts it takes to not win anything ie. the time you waste flipping coins instead of spending time with people. I feel embarrassed for spending as much time as I did on this. At least I learned something… savings after 1 heads: 1.5 percent profit: 50.0 ....money after loosing n times after: 0.75 savings after 2 heads: 2.25 percent profit: 125.0 ....money after loosing n times after: 0.5625 savings after 3 heads: 3.375 percent profit: 237.5 ....money after loosing n times after: 0.421875 savings after 4 heads: 5.0625 percent profit: 406.25 ....money after loosing n times after: 0.31640625 savings after 5 heads: 7.59375 percent profit: 659.375 ....money after loosing n times after: 0.2373046875 savings after 6 heads: 11.390625 percent profit: 1039.0625 ....money after loosing n times after: 0.177978515625 savings after 7 heads: 17.0859375 percent profit: 1608.59375 ....money after loosing n times after: 0.13348388671875