Betting
Posted by matijs 20/09/2018 at 09h03
I happened upon this comment.
But more important, it just doesn’t work sensibly to explain why many people decline modest bets (e.g. that someone not on the brink of starvation would decline a 50/50 lose $100 vs gain $110) bet.
You can look at this bet in two ways. The first is the single bet. Then, you can think about how bad you feel about losing $100, versus how good you feel about gaining $110.
The second way is as a repeated bet. And I think this is how people do think about it: If I bet yesterday, why not bet today? Or, I lost yesterday, I need to bet again today to ‘make up for it’.
Emotions aside, the reason given that the bet is a good one, is that in the long run the better will come out ahead. But how long is the long run?
Let’s fire up irb. (I’ve reformatted the lines a bit to fit in an article layout.)
>> def bet; rand < 0.5 ? -100 : 110; end
>> count = 0; sum = 0; while sum < 1; count+= 1; sum += bet; end; [count, sum]
=> [81, 90] # Oops!
>> min = 0; count = 0; sum = 0; \
> while sum < 1; count+= 1; sum += bet; min = sum if sum < min; end; \
> [count, min, sum]
=> [35, -530, 70] # OOPS!
Maybe you can spare $100, but can you spare $530? (Not to mention the fact that many people can’t spare $100.).
Or even $1340, leading to a $50 win after 136 bets?
=> [136, -1340, 50]
What are the chances of a repeated bet ruining you before you gain anything at all?
>> def compound_bet; min = 0; count = 0; sum = 0; \
> while sum < 1; count+= 1; sum += bet; min = sum if sum < min; end; \
> [count, min, sum]; end
>> def killer_bet(threshold); count, min, sum = compound_bet; min < -threshold; end
>> def killer_chance(threshold); 100000.times.select { killer_bet(threshold) }.count / 1000.0; end
>> killer_chance(500) #=> 8.017
>> killer_chance(1000) #=> 3.532
A betting scheme with a 3.5% chance of losing $1000 doesn’t sound so good…
(The commenter goes on to point to an article that actually doesn’t make the claim that the given debt is a ‘modest debt’, and seems far more interesting than that.)