Any low win rate is psychologically devastating and almost certainly will not be followed through to get the 10% winners. What is the lowest win rate that you would be psychologically willing and able to follow?
Sorry, I didn't realize you are British. Anyway here in the USA, there are two big multi-state lotteries and you can calculate the break-even jackpot (bejp) of each. For example the bejp of the MegaMillions lottery, ignoring taxes and the lumpsum-versus-annuity nonsense, is $143,739,648 (based on the current odds in Wikipedia). $1G/bejp = 6.96 So ignoring taxes and the lumpsum-versus-annuity nonsense, you should buy no more than six tickets for a $1G MegaMillions jackpot. Considering taxes and if you want the lump sum, this number drops to four or less.
Can you elaborate on this? How can I consider a setup with a negative expectation over the long run? It is about the long run not getting lucky on Tuesday!
Yes, I would. I see little diference in my life between having $50 million and a billion. Since the $50,000,000 does not tempt me why should the nice fat round number get me excited!
Unless you and Visaria are the same person, I wasn't talking to you. And most people see a lot of difference between 50 million and a billion dollars.
Use a PM if you want to reach someone privately. Most people probably do see a world of difference between the 50 mil and a billion yet my guess is if they give it some thought many will see that the change in circumstance is so significant that the difference in the quality of their lives is not to great.
The first setup is far more attractive because the higher win rate lowers the likely drawdown, and thus you can trade it on much more size for the same risk.
It can be proven easily by using the Kelly formula, or with a little effort by using Monte Carlo runs.
You got the basic Kelly formula wrong. Kelly fraction is 12.7% for the first setup, 5.5% for system B. System A: Kelly = (.55*(433/407+1)-1)/(433/407) = 12.7% System B: Kelly = (0.1*(1000/50+1)-1)/(1000/50) = 5.5%