3 ms·
You are ignoring half of the possible outcomes. If you get HH or TT, that's $2.25 and 0.36, which averages to $1.25. 50% of ($1.25 + $.90) for a $1 bet seems l
by gowld 7y ago
You are ignoring half of the possible outcomes. If you get HH or TT, that's $2.25 and 0.36, which averages to $1.25.
50% of ($1.25 + $.90) for a $1 bet seems like a great game to play.
- zawerf 7y agoAfter many rounds, you expect to see half heads and half tails. In that case your outcome at n rounds would be around 1.5^n/2 * 0.6^n/2 = 0.9^n/2 which trends towards zero. You would need around 26% more heads than tails just break even (0.6*(1.5^1.26)=1). But even if you were lucky at first, you will always "regress toward the means" in terms of head to tails ratio if you kept playing.
- yellowstuff 7y agoThis is actually an awesome illustration of why a lot of famous results in academic finance were wrong in the 70s and 80s. Returns don't average, they multiply. If you get HHTT or TTHH you're in terrible shape: 2.25 * .36 = .36 * 2.25 = .81 You started with $1 and now have 81 cents. I recently learned that a lot of early computer-era academic finance actually made the same error of averaging returns, as described in Finding Alpha: http://falkenblog.blogspot.com/2016/08/finding-alpha-pdf.html http://falkenblog.blogspot.com/2016/08/finding-alpha-pdf.htm...