do you think you could only win the game by chances ?

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do you think you could only win the game by chances ?

Here are some links that might be useful to you:

https://betterexplained.com/articles/understanding-the-monty-hall-problem

https://betterexplained.com/articles/understanding-the-monty-hall-problem
Understanding the Monty Hall Problem – BetterExplained
Surprisingly, the odds aren’t 50-50. If you switch doors you’ll win 2/3 of the time! Today let’s get an intuition for why a simple game could be so baffling. The game is really about re-evaluating your decisions as new information emerges. Play the game. You’re probably muttering that two doors mean it’s a 50-50 .

https://www.statisticshowto.com/probability-and-statistics/scratch-off-odds

https://www.statisticshowto.com/probability-and-statistics/scratch-off-odds
Scratch Off Odds: How to Increase Your Probability of Winning
You can increase your chances by buying 10 at a time, but it’s not a guarantee of a win. Scratch offs are very much a game of chance: I bought ten in a row. And they were all losers. There is another very good reason for buying cards all from the same game. The probability of winning increases every time you buy more tickets for the same .

https://www.dummies.com / article / business-careers-money / business / accounting / calculation-analysis / applying-probability-games-chance-254799

https://www.dummies.com / article / business-careers-money / business / accounting / calculation-analysis / applying-probability-games-chance-254799
Applying Probability to Games of Chance – dummies
The probability of rolling a four is 1/6. You have three dice involved, so to find the probability of all three rolls resulting in a four, use the multiplication property and get. This is about 0.5%. The chance is slight. If you’d be happy with having the three dice be the same, not caring about which number, then you add the six …

https://www.khanacademy.org/math/statistics-probability/probability-library/basic-theoretical-probability/v/monty-hall-problem

https://www.khanacademy.org/math/statistics-probability/probability-library/basic-theoretical-probability/v/monty-hall-problem
The Monty Hall problem (video) | Probability | Khan Academy
So you have to think that this could also be defined as a game of eliminating goats. This does not guarantee that the car will be behind door 2, but given 2 opportunities to eliminate goats, chances are you can’t eliminate them by maintaining the same choice always.

https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:prob-combinatorics-precalc/v/permutations-and-combinations-4

https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:prob-combinatorics-precalc/v/permutations-and-combinations-4
Example: Lottery probability (video) | Khan Academy
4p4/60p4 = same answer. explanation: think of this top part of the probability (numerator) as 4p4 since you have 4 numbers to pick from and you want to pick 4 numbers, the number of ways you can pick 4 numbers from 4 numbers is 4*3*2*1. 4p4. This gives you the total number of non-unqiue ways to choose these numbers.

https://www.scientificamerican.com/article/bet-on-the-losing-team

https://www.scientificamerican.com/article/bet-on-the-losing-team
Bet on the Losing Team | Scientific American
If your team is up by 4, chances are it will hold on for the victory (around a 70% chance). If your team brings a 6 point lead into the locker-room then the chances of a win go up to 80…

https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory:_A_Discovery_Approach_(Nordstrom)/02:_Two-Person_Zero-Sum_Games/2.03:_Probability_and_Expected_Value

https://math.libretexts.org/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory:_A_Discovery_Approach_(Nordstrom)/02:_Two-Person_Zero-Sum_Games/2.03:_Probability_and_Expected_Value
2.3: Probability and Expected Value – Mathematics LibreTexts
Consider a game where you toss two coins. If you get two Heads, you win ($2). If you get a Head and a Tail, you win ($1), if you get two Tails, you lose ($4). Find the expected value of the game. (Caution: first you need to find the probability of each event- think about equally likely events.)

https://artofproblemsolving.com/blog/articles/the-math-of-big-money-lotteries

https://artofproblemsolving.com/blog/articles/the-math-of-big-money-lotteries
The Math of Big-Money Lotteries: Your Chances of Winning the Powerball …
Normally there would be 4! (pronounced four factorial and equal to 4 x 3 x 2 x 1 = 24) ways for a four-digit number to be ordered, but the repeated 8 gives 4!/2!, or 12, possibilities out of the 10,000 in the game. So the chance of winning this way is about 1 in 833. While the odds are better, the prizes tended to be lower as a result.

https://www.oreilly.com/library/view/head-first-statistics/9780596527587/ch04.html

https://www.oreilly.com/library/view/head-first-statistics/9780596527587/ch04.html
4. Calculating Probabilities: Taking Chances – Head First Statistics [Book]
1 – (1/18 + 1/18) = 8/9 = 0.889 (to 3 decimal places) The probability of the ball landing in pockets 1, 2, 3, or 4. The probability of each pocket is 1/38, so the probability of this event is 4 x 1/38 = 4/38 = 0.105 (to 3 decimal places) Get Head First Statistics now with the O’Reilly learning platform. O’Reilly members experience books …

https://nrich.maths.org/4735

https://nrich.maths.org/4735
Taking Chances – NRICH
When you play a game lots of times, what happens on average is very important. If there are two possible rewards, 2 and 8, and they are equally likely, the average prize is 5. But suppose you tend to win 2 twice as often as you win 8. So your chances are 2/3 and 1/3 of winning 2 and 8. Your series of winnings might begin:
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