Forum Thread

This article goes through all the math on how these probabilities were determined. If you simply want to know the probabilities, and the best amount of rounds to grind game chips, scroll down to the bottom.


In order to calculate the chances of you winning a given amount of higher or lower rounds, first you have to calculate the average chance of winning (or losing) each round. To do this, I assumed the player would choose the best option each time (If he says 2-5, pick higher, If 6-9, pick lower). This gives over a 50% probability of victory each time.


Win chance for ONE round of Higher or Lower, based on his first number pick(Percentages rounded):

2 - 8/9, 89%

3 - 7/9, 78%

4 - 6/9, 67%

5 - 5/9, 56%

6 - 5/9, 56%

7 - 6/9, 67%

8 - 7/9, 78%

9 - 8/9, 89%


If you average all these probabilities together by adding the numerators together and dividing by 8, you get a 6.5/9 chance of winning by average, taking into account all possible first numbers. However, due to this being an illegal fraction, I will simplify it to a 13/18 chance for the next segment.


Now for the tricky part: Figuring out how often you will go MULTIPLE rounds without losing. To do this, I had to calculate the probability of you losing at least once in a game of higher or lower. Well, calculating this is actually the same as calculating if you win every time! The formula for this is 13/18^n, with n being the number of rounds played.


Rounds Played:

1 - 13/18, 72%

2 - 52% (Stopped doing fractions due to them being ridiculously complicated)

3 - 38%

4 - 27%

5 - 20%

6 - 14%

7 - 10%

8 - 7%

9 - 5%

10 - 4%

11 - 3%

12 - 2%

13 - 1.5%

14 - 1%

15 - 0.8%


Soooooooooo... If you ever wondered why it's so hard to get 15 in a row, this is why. After getting these stats however, I decided to try to find the average turn out of tokens for each amount of rounds, so that I can find the best amount of rounds to play for token grinding.


This is pretty simple. Taking the percentage of victory(as a decimal), and multiplying it by the amount of tokens you would get for winning the round (Which is bet amount x token multiplication factor), you can see what amount of rounds would likely be best to earn tokens from, based on what you would probably get from multiple games playing that amount of rounds(in comparison to what you started with): (For this I used a bet amount of 1000 tokens to show the comparison)


1 - 360 tokens

2 - 416 tokens

3 - 456 tokens

4 - 459 tokens

5 - 460 tokens

6 - 420 tokens

7 - 380 tokens

8 - 329 tokens

9 - 285 tokens

10 - 272 tokens

11 - 240 tokens

12 - 186 tokens

13 - 161 tokens

14 - 122 tokens

15 - 110 tokens

Conclusion: Based on this data, I can conclude that this game is absolutely TERRIBLE for long term game chip earning, and probably should only be done for quests or for fun, due to you likely being left off with less than half of what you started with. If you decide to try anyway, play 3-5 rounds to maximize your chances of winning and how many you earn at the same time. If you get a quest to beat multiple rounds in a row, understand the chances because it could take a while. And, remember that every time you click to do another round, you have a 5/18 chance of losing, so ask yourself if it is worth that risk. Anyway, hope this was interesting to all you fellow trainers at the game center, and tell me how wrong my math was XD Thanks for reading! :P

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Yes, Higher or Lower is one of the worst gambling games in my opinion. I usually always do coinflip, because how bad the chances are. Would you rather have a 20% chance to get 23,000 chips? Or a 50% chance to get 20,000 chips?

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