Probability of winning spin the wheel of this kind

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boyguy

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chance of profiting spin the wheel where numbers 1 to 10 and if I bet $1 I win $8 plus my $1 bet making a total of $9 return.


So my idea would be to bet on 8 numbers there by giving me 80% chance of winning a profit of $1 and 20% chance of losing $8 would this be a good strategy in the long run? what is the expected value?
 
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boyguy said:
chance of profiting spin the wheel where numbers 1 to 10 and if I bet $1 I win $8 plus my $1 bet making a total of $9 return.
Click to expand...
I'm sorry, but I don't understand...? I think some information is missing...? How many numbers are on this wheel? Is it a "fair" wheel (that is, do all numbers have an equal probability of being spun)? What is the definition of a "win"?

Please reply with the full and exact text of the original exercise, the complete instructions, and a clear listing of your thoughts and efforts so far, so we can try to figure out what's going on. Thank you! ;)
 
There are 10 numbers on the wheel all with equal chance of being spun... If you bet 1 dollar you will have a return of 9 dollars in total.. so that is a profit of 8 dollars... if not then you lose 1 dollar which is your bet..

So my question is would betting 8 numbers out of 10 numbers be a good idea? makes sense since that will give you a probability of 80% chance of winning and 20% chance of losing (the 2 numbers you did not bet on) and only targeting a 1 dollar profit but giving you a 20% chance of losing 8 dollars
 
boyguy said:
There are 10 numbers on the wheel all with equal chance of being spun... If you bet 1 dollar you will have a return of 9 dollars in total.. so that is a profit of 8 dollars... if not then you lose 1 dollar which is your bet..

So my question is would betting 8 numbers out of 10 numbers be a good idea? makes sense since that will give you a probability of 80% chance of winning and 20% chance of losing (the 2 numbers you did not bet on) and only targeting a 1 dollar profit but giving you a 20% chance of losing 8 dollars
Click to expand...
By "betting eight numbers", do you mean that you'd be putting one dollar on each of eight numbers, so you're buy-in to the game is $8?
 
boyguy said:
There are 10 numbers on the wheel all with equal chance of being spun... If you bet 1 dollar you will have a return of 9 dollars in total.. so that is a profit of 8 dollars... if not then you lose 1 dollar which is your bet..

So my question is would betting 8 numbers out of 10 numbers be a good idea? makes sense since that will give you a probability of 80% chance of winning and 20% chance of losing (the 2 numbers you did not bet on) and only targeting a 1 dollar profit but giving you a 20% chance of losing 8 dollars
Click to expand...

You've almost done the calculation for the expected value, which is what you initially asked about!

80% of the time you spend $8 and get back $9, gaining $1;
20% of the time you spend $8 and get back nothing, losing $8.
​

Do you see how this fits into the definition of expected value? Do it. You'll find it is negative, because you are losing money in the long term. That's how games like this are always set up.
 
So what would be a good strategy to win this game consistently? since the payout is 8x what you bet...
 
what about if I just bet on 1 number through out the game? would I win more in the long term?
 
boyguy said:
what about if I just bet on 1 number through out the game? would I win more in the long term?
Click to expand...
Try working the "expected value" process for various bets. See what you can figure out.... ;)
 
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