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# Calculating Overall Odds

If you have a game that increases in difficulty with each turn, you'll have different odds of winning each turn. But how do you mathematically calculate overall odds? For example: Round 1: 100% chance to win the round Round 2: 90% chance to win the round Round 3: 80% chance to win the round Round 4: 70% chance to win the round Round 5: 60% chance to win the round But with every round, if you lose, the whole game is over. Playing 1 round is a sure thing. Playing two rounds it is possible to lose. Play 5 rounds and you are very likely to lose. It works out to be a 60% chance of 70% of 80% of 90%. Is there some sort of algorythm that would give you the cumulative odds of winning a six round game? The result would be less than 60% because you could have lost on one of the previous rounds. Calculating it the way I described it feels like a horribly inefficient brute-force method. There's got to be an elegant formula for this.

8th Jun 2021, 7:59 PM
Jerry Hobby
3 Respuestas
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Can't we multiply all odds cause to win all 6 rounds we have to win each of them so winning first round and winning second round........ So there is and so we can multiply them to find answer 1*9/10*8/10*7/10*6/10*5/10 =15120/100000 =15.12% Is it right or I get something wrong??
9th Jun 2021, 1:18 AM
YUGRAJ
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Seems rigth to me
9th Jun 2021, 8:57 AM
YUGRAJ
0
I had trouble applying the suggestion, but I think I was inspired enough to work it out. Please check the code and see if you have any suggestions / corrections. Thank you @YUGRAJ. https://code.sololearn.com/cA11A8A0A9a1
9th Jun 2021, 5:03 AM
Jerry Hobby