Hi, I'm back with another beginner level question that my pride makes it a little embarrassing to ask. But it's much better to ask it now, then wait till I'm too embarrassed to ask at all!
This is something I've I haven't heard addressed explicitly in the way I'm going to put it since it's pretty simple. I'm pretty sure I already know the answer, but would just like someone to confirm and add comments (however, I'd would find it more interesting if I didn't have it right).
If you have two different bets (in general, not blackjack bets in particular) with the same edge, does the bet with the lower probability always have a higher variance?
I've always took the variance/standard deviation of a game to refer to the units won or loss, but I suppose authors sometimes refer to other related variables or qualify them in different ways (win & loss per units bet or per hand). So my thinking is that it's much easier for a 1 in 10 bet to be off of expectation than a 50/50 one. For example imagine both have 0 edge and bet is wagered 10 times. It seems to me that it's more likely that you'll be down 4 units in the 1 in 10 than being down 4 units in the 50/50 proposition. I could go on to describe my thinking further, but the rest is probably either redundant or obvious.
Please let me know if I'm missing something, thanks!
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