Probability as it relates to bankroll

[Yobz]

My sociology professor wanted to prove a point about risk and how people react to it (more psychology, but it related to what we are talking about). Anyway, she put these stats up on the projector:
18% of people chose to have a 45% chance of winning 6,000
82% of people chose to have a 90% chance of winning 3,000
Even though the expected values are the same, people chose the one with higher probability more.
On the other hand, we have a similar situation:
78% of people chose to have a 0.001% chance of winning 6,000
22% of people chose to have a 0.002% chance of winning 3,000
Once again, the expected value is the same, but the voting was clearly skewed.

I argued, in the first case, that it makes sense to chose the 3,000 with 90% chance because you only get 1 try and you start with a bankroll of 0 while she kept insisting that it did not make a difference. Who is right (along w/the math please) and what about the second situation?

Thanks guys, first post in probability /images/graemlins/smile.gif

[chris_a]

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Who is right (along w/the math please) and what about the second situation?

[/ QUOTE ]

Nobody's right or wrong. The point seems that when it's not a sure thing (0.001% chance of winning), that people seem to go for the higher number because they aren't expecting it anyway. But when it's almost a sure thing, people seem to go with the one that wins more often so they won't be dissapointed. As far as EV goes, there's no difference and it's purely psychological.

As far as bankroll, there's no situation where you're losing money here anywhere so necessary bankroll is not an issue. Just keep playing.

If you want to maximize something other than EV, then you might prefer one over the other.

[tommo]

the only argument I can see for choosing the higher percentage (90% for 3000) is if you can use that 3000$ too make more money. and you couldn't use the 6000$ to make twice as much money.

[irchans]

Generally speaking, if you have a series of investment choices to make that all have the same expected value, then your risk of bankruptcy is reduced if you always choose the investments with the smaller standard deviation.

Thus 90% chance of $3000 is the better investment.

Standard Deviations:
Sqrt[ 0.9* 300^2 + .1*2700^2 ] = $900
Sqrt[ 0.45* 3300^2 + .55*2700^2 ] = $2984.96

[Paul2432]

In life one should maximize utility not money. I'll give a simple example. Would you rather have a 10% chance of $1 billion or 100% chance of $50 million? For most ordinary people, the decision is simple. Take the $50 million, even though it has half the EV.

The same principle applies in your professors example.

Paul