Guess the Gap Game

[LeMansLambo14]

The rules are simple:

One person states the track, game mode, tunes, drivers, approximate time (around 2 seconds), and the two cars in GT7. The goal is not to guess the actual lap time, but rather the gap between the two cars. Note that the times (not stated) can be set in any way between two cars, whether at a race finish or time trial mode.

So I'll start with my question, than someone guesses a gap, I'll give a hint, than someone else guesses, repeat.

They'll be a one week entry period for the question, and the person who comes the closest wins!

Once the winner has been nominated by the person who posted the question, it is then the winners turn to post a question.

Please post your question in a similar format to my one below:

Round #1:
Entry period 27th Sept -4th Oct.

Track: Monza, chicanes
Game mode: Time trial
Cars: Honda NSX '17, Nissan GT-R '17 (both stock)
Drivers: Me in the NSX, my bro in the GT-R
Approximate time: 1:57.500-2:00.000

Now guess the gap!

 

[eran0004]

Assuming that the gap is within a second it seems like the game is essentially about guessing a random number between 0 and 1000 over and over until you get it right. There's no information provided that will help you make an educated guess.

The most efficient strategy would be to establish a lower and an upper boundary and then keep cutting the interval in half until the error is less than one millisecond.

 

[Talon16]

 

[LeMansLambo14]

Assuming that the gap is within a second it seems like the game is essentially about guessing a random number between 0 and 1000 over and over until you get it right. There's no information provided that will help you make an educated guess.

The most efficient strategy would be to establish a lower and an upper boundary and then keep cutting the interval in half until the error is less than one millisecond.

You could make an educated guess by testing it in GT7 yourself, as this is a game involving it. To make it easier though, I'll add a upper and lower limit of around 2 sec. Remember, I'll give hints like "higher" or "lower" too, so think of it more of a "hot-cold" game

 

[eran0004]

You could make an educated guess by testing it in GT7 yourself, as this is a game involving it. To make it easier though, I'll add a upper and lower limit of around 2 sec. Remember, I'll give hints like "higher" or "lower" too, so think of it more of a "hot-cold" game

There's no way to make an educated guess because the skill and performance of the drivers are unknown. This makes the gap between the cars a random noise. We can probably make a guess which car is faster, assuming that the drivers are on a similar skill level and are competent enough to drive these cars without excessive loss of traction or control, but there's no way of making an educated guess about the gap down to the millisecond.

With an initial interval of two seconds, the probability of guessing correctly on the first attemp is 1/2001.

The best approach is to guess a gap of 1.000 seconds, to cut the interval in half.

Let's say the gap is greater, then our next guess should be 1.500 seconds. It has a probability of 1/1000.

If the gap is smaller we guess 1.250, with a probability of 1/499.

Let's say the gap was smaller again, now we guess 1.125. The probability that it's correct is 1/249 so we are still highly unlikely to have found the right answer.

We continue to cut the interval in half until we find the right answer. If 1.125 was too high, we guess:

#	Min	Max	Guess	Probability	Result
5	1.001	1.124	1.062	1/124	Higher
6	1.063	1.124	1.094	1/62	Lower
7	1.063	1.093	1.078	1/31	Lower
8	1.063	1.077	1.070	1/15	Lower
9	1.063	1.069	1.066	1/7	Higher
10	1.067	1.069	1.068	1/3	Lower
11	1.067	1.067	1.067	1	Correct!

With this optimal strategy it would take somewhere around 10 guesses to get the right answer. If you guess randomly it could take hundreds of guesses.

Since the optimal strategy is always the same, each round of the game would be the same and every guess would be predetermined. Sometimes you might be lucky and find the answer within 7 rounds, but most of the time you'd need 10 guesses – assuming that you play with the optimal strategy.

 

[LeMansLambo14]

There's no way to make an educated guess because the skill and performance of the drivers are unknown. This makes the gap between the cars a random noise. We can probably make a guess which car is faster, assuming that the drivers are on a similar skill level and are competent enough to drive these cars without excessive loss of traction or control, but there's no way of making an educated guess about the gap down to the millisecond.

With an initial interval of two seconds, the probability of guessing correctly on the first attemp is 1/2001.

The best approach is to guess a gap of 1.000 seconds, to cut the interval in half.

Let's say the gap is greater, then our next guess should be 1.500 seconds. It has a probability of 1/1000.

If the gap is smaller we guess 1.250, with a probability of 1/499.

Let's say the gap was smaller again, now we guess 1.125. The probability that it's correct is 1/249 so we are still highly unlikely to have found the right answer.

We continue to cut the interval in half until we find the right answer. If 1.125 was too high, we guess:

#	Min	Max	Guess	Probability	Result
5	1.001	1.124	1.062	1/124	Higher
6	1.063	1.124	1.094	1/62	Lower
7	1.063	1.093	1.078	1/31	Lower
8	1.063	1.077	1.070	1/15	Lower
9	1.063	1.069	1.066	1/7	Higher
10	1.067	1.069	1.068	1/3	Lower
11	1.067	1.067	1.067	1	Correct!

With this optimal strategy it would take somewhere around 10 guesses to get the right answer. If you guess randomly it could take hundreds of guesses.

Since the optimal strategy is always the same, each round of the game would be the same and every guess would be predetermined. Sometimes you might be lucky and find the answer within 7 rounds, but most of the time you'd need 10 guesses – assuming that you play with the optimal strategy.

Thank you for the insight, I'll reconsider how the game should be played; I didn't think it would take so much to get the correct answer. I'll work it out soon.

If someone else has any thoughts, I'd appreciate it please

 

[eran0004]

Thank you for the insight, I'll reconsider how the game should be played; I didn't think it would take so much to get the correct answer. I'll work it out soon.

If someone else has any thoughts, I'd appreciate it please

When there are so many possible guesses, what usually works is to have the winner be the person whose guess is the closest to the right answer. Say you give people one week to submit guesses and then you pick the winner.

 

[LeMansLambo14]

When there are so many possible guesses, what usually works is to have the winner be the person whose guess is the closest to the right answer. Say you give people one week to submit guesses and then you pick the winner.

That's a great idea, thanks for the tip @eran0004

I've edited the original post