Percentage question (probability , game)

In summary, the conversation discusses the concept of probability in games of chance and how it is calculated. It also explains the difference between odds and probability and provides tips on how to improve one's chances of winning. The conversation also touches on the concept of "house edge" in gambling and how it affects the casino's profits.
  • #1
reenmachine
Gold Member
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8
Suppose you throw a dice and on the first throw you win if you score 1 , you lose if you score 2 & 3 and have to throw the dice again if you hit 4 , 5 or 6.If you have to throw the dice again the rules changes and you win if you hit 1 but lose if you hit 2.If you hit any other number , you continue to throw it until you win or lose (with the same rules as the second throw).How do I find out what are my odds to the nearest percentage of winning in this game before the first throw?

I tried this , please help me understand what I did wrong or what I did right:

First throw:

1/6 = win (16,67%)
2/6 = lose (33,33%)
3/6 = throw again (50%)

Second throw and beyond:

1/6 = win (16.67%)
1/6 = lose (16.67%)
4/6 = throw again (66.67%)

Since the odds are the same for winning or losing beyond the first throw , once I get passed it my odds becomes 50% to win overall.

Calculations(?):

50(0,50) + 16,67(1) + 33,33(0)
25 + 16,67 + 0 = 41,67 = 42%

any thoughts would be appreciated , I'm pretty insecure everytime I encounter a probability problem so go easy on me please :)
 
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  • #2
Calculation looks OK. Style question - why did you use comma for decimal points?
 
  • #3
mathman said:
Calculation looks OK. Style question - why did you use comma for decimal points?

Thanks a lot , I had no idea how to attack the problem , I have almost no background in probability so I just went with my intuition.

As for the style question , I guess I always used commas since my youth.Is this considered wrong or is it just a computer problem? I rarely use computers to do or communicate mathematics.Do the vast majority of programs don't count the commas as decimal numbers? If that's the case I guess the more math I'll do on computers the more I'll have to change that habit ;)
 
  • #4
(Out of context , but if on a random first throw (ignoring the previous problem and rules)):

If I have a 25% chance to have a 25% chance to win on my next throw , a 60% chance to have a 60% chance on my next throw , and a 15% chance to have a 15% chance on my next throw , how do I calculate my odds of winning on my next throw?

I tried:

25(0.25) + 60(0.60) + 15(0.15)
6.25 + 36 + 2.25 = 44.5%
So I would have a 44.5% chance to win on my next throw.

does that make any sense to you guys?

thanks
 
  • #5
N.B.: In most English speaking countries, the decimal point is a dot (.), whereas on the Continent it is a comma (,). The separator for thousands is the opposite.

A similar situation occurs with dates: in the US, it is month-day-year; elsewhere day-month-year.
 
  • #6
Ok I'll ask it here also even though I asked it in the homework subforum , but if I have a 5.7% chance to win and a 8.33% to lose a game (with the additionnal 85.97% meaning I have to roll the dice (or whatever) again with the same odds until I win or I lose , how do I calculate my odds of winning the game overall before the game even begins?

In the other thread they talked about conditionnal probabilities , a concept I'm not knowledgeable about.

I thought my odds of winning were 40.6% because of 5.7+8.33=14.03. 5.7/14.03*100 = 40.6 , but it seems I was wrong.

If I have to add up the probability of winning round 1 + P of winning round 2 etc... how do I do it?

My try:

round 1: 0.057
round 2: 0.8597 (0.057)
round 3: 0.8597 (0.8597)(0.057)
etc...

I have a very strong feeling that I'm wrong , and even if I'm right how do I know when to stop adding up? (can't add up forever)

thanks!
 
  • #7
reenmachine said:
I thought my odds of winning were 40.6% because of 5.7+8.33=14.03. 5.7/14.03*100 = 40.6 , but it seems I was wrong.

No, that's correct.

reenmachine said:
round 1: 0.057
round 2: 0.8597 (0.057)
round 3: 0.8597 (0.8597)(0.057)
etc...

I have a very strong feeling that I'm wrong , and even if I'm right how do I know when to stop adding up? (can't add up forever)

You are right again! The trick is that you can add up forever, this is called the sum of a geometric series
whose properties are well known. In this case the sum is ## \frac{0.057}{1-0.8597} = \frac{0.057}{0.1403}##, just the same as your intuitive result.
 
Last edited:
  • #8
wow I'm actually impressed that I was right :D

Last question , very basic , but 40,6% is the odds of winning right? If I used the word probability instead of odds , would the result be the same?

Thank you for your input :X

cheers
 
  • #9
reenmachine said:
wow I'm actually impressed that I was right :D

Last question , very basic , but 40,6% is the odds of winning right? If I used the word probability instead of odds , would the result be the same?

Thank you for your input :X

cheers

Don't get caught up in language quibble. Odds of winning and probability of winning are the same.
 

FAQ: Percentage question (probability , game)

What is the probability of winning in a game of chance?

The probability of winning in a game of chance is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

How do you calculate the percentage of a given number?

To calculate the percentage of a given number, you can use the formula (percentage/100) * number. For example, to calculate 25% of 80, you would use the formula (25/100) * 80 = 20.

What is the difference between odds and probability?

Odds and probability both measure the likelihood of an event occurring, but odds represent the ratio of favorable outcomes to unfavorable outcomes, while probability represents the ratio of favorable outcomes to all possible outcomes.

How can I improve my chances of winning in a game of chance?

The outcome of a game of chance is ultimately random, but you can improve your chances by understanding the odds and making informed decisions. It is also important to set a limit on the amount of money you are willing to spend and to stick to a strategy.

What is the "house edge" in gambling?

The "house edge" is the built-in advantage that a casino or gambling establishment has in a game of chance. It is the percentage of each bet that the casino expects to keep over time. This is how they make a profit.

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