In the newest Card Player magazine, DS has a probability quiz.
One of the questions:
You have $100 to your name for the next few days and are contemplating betting it all on a 60% shot getting even money.
But if you wait until tomorrow, you can bet that $100, but no more, on an 80% shot.
Should you wait? What if the second bet was 70%?
His answer:
Wait for the 80% shot but not the 70% shot. It's simple algebra related to "expected value".
Based on the only the information given in this question, I can't imagine how it isn't best to wait for the 70% bet.
But it doesn't take any algebra to figure that out, so I'm guessing something was missing from the article.
If you take the 60%, then reinvest $100 in the 70%, you get:
EV = 0.60*(100 + 0.70*200) = $144
Because: 60% of the time you double up today and end up with a lock on $100 (which you can't bet further) plus 70% chance to double the remaining $100. If you run the same equations for the 80% case, you get $156 if you take the 60% and $160 if you wait, so you should wait.
Except that it only says you can bet if you wait until tomorrow. It doesn't say you can do anything if you bet today. No reason to think you could ever bet more than once.
But what you said is probably what he meant; either something was missing or it's just very poorly worded.
And even your solution doesn't require algebra, so who knows.
This is more a reading comprehension problem than probability:
Quote:
You have $100 to your name for the next few days and are contemplating betting it all on a 60% shot getting even money. But if you wait until tomorrow, you can bet that $100, but no more, on an 80% shot.
Should you wait? What if the second bet was 70%?
That 'But' clause makes the first sentence and second sentence mutual exclusive. You cannot make 2 bets. $100 today on a 60% favorite or $100 tomorrow on an 80% favorite. You should wait. If the second option is anything above 60% (e.g. 70% or even 60.01%) you should wait.
The math is easy, now let the semantic arguments begin.
This is more a reading comprehension problem than probability:
That 'But' clause makes the first sentence and second sentence mutual exclusive. You cannot make 2 bets. $100 today on a 60% favorite or $100 tomorrow on an 80% favorite. You should wait. If the second option is anything above 60% (e.g. 70% or even 60.01%) you should wait.
The math is easy, now let the semantic arguments begin.
In the newest Card Player magazine, DS has a probability quiz.
One of the questions:
You have $100 to your name for the next few days and are contemplating betting it all on a 60% shot getting even money.
But if you wait until tomorrow, you can bet that $100, but no more, on an 80% shot.
Should you wait? What if the second bet was 70%?
His answer:
Wait for the 80% shot but not the 70% shot. It's simple algebra related to "expected value".
Based on the only the information given in this question, I can't imagine how it isn't best to wait for the 70% bet.
But it doesn't take any algebra to figure that out, so I'm guessing something was missing from the article.
For some reason the question omitted the fact that you can make the second bet if you make the first bet and win it.
