Adjusting risk

Bloomberg:

Bloomberg

Consider making this probability distribution.   You are flipping a coin.  There are really only seven distinct values, to accuracy you would flip the coin dour times.  The rare events, the once on ten year events are events where you rolled the dice heads four times.

But the distribution is skewed. We get no returns more often than the extreme return.  q > p.

 We want to modify the terms in the distribution to make it look like a centered distribution with a fair coin. We have to bet more on the tail end and bet less where it is skewed left. Treat the distribution like four options, you can bet a zero return or p^1 ... to p^4.  Make your bet equal to some b^k for each term, b > 1 and the total return can look like a fair coin flip.