One factor I do not love to do anymore is to start out with the variety of 50. For some time, I used to be favoring beginning with 48. But proper for the time being that I’m wrote this textual content, my most popular first quantity can be… 32.

Yeah, that runs me into bother a bit over a 3rd of the time, however I’m at present considering that’s higher (extra rewarding) than some other strategy I’ve tried to this point.

Now, I occur to have studied this a bit, and, as I mentioned, I want to share my evaluation with no additional delay:

][CyberPillar][ Legend of the Red Dragon sub-section: guessing a number in six tries

(It’s a sub-section of the LoRD page, which shows some output from the mini-game I described momentarily.)

I’ve actually tried this puzzle numerous times before, because this is essentially a mini-game within a larger game called “Legend of the Red Dragon”. For those who don’t know about “Legend of the Red Dragon”, it was a multiplayer computer game that was installed on many BBSs. A BBS was a computer system that acted like a server for people using “dial-up” modems to connect directly to servers via phone lines, which was a common approach before widespread Internet access had people connecting to centralized sources that relayed information through multiple servers.

So, there’s every reason to believe/suspect that the original poster may have been seeking to gain some advantages in a game.

To all those who used information theory, binary logic, tree splitting, and describing functions like “ $lceil log_2 (n+1)rceil$ ”, I thank you for your input. And, I mean that sincerely: you provided details to answer the question that was asked, and so your answer was entirely on-topic and an appropriate answer to the question that was asked. So your answers were not wrong; they just aren’t as useful for every possible usage scenario, including the scenario that I just brought up. But their answers were completely suitable for the question that was originally asked, and would be more useful in other scenarios.

Such answers not only answered the question that was asked, but help to provide additional information. For instance, such approaches lets us know, “what is a minimum number of guesses that would be required to guarantee a successful guess?” And, strategies of simply splitting the numbers may result in getting really, really close after six guesses. The final permitted guesses may be so close, in fact, that the next guess would be an absolutely guaranteed right answer. These seem like things that could be useful in some scenarios, so I don’t wish to dismiss the good of the approaches that were taken.

That’s all nice and interesting information. However, I wished to share my analysis, because it provides some more details that would be helpful to answer another question: “What is the strategy that will provide the right answer most of the time?” Because, you see, in the embedded mini-game I’m referring to, we really don’t care about getting close to the right answer. That might be great for some usage scenarios, where guessing a number that is close to being accurate is way, way better than a number that is way, way far away from being accurate. However, in the usage scenario I’m describing, all we care about is getting 100% accurate as often as possible. Because, getting the accurate answer leads to the embedded mini-game providing a reward, and being even slightly inaccurate results in no reward whatsoever. A series of six missed guesses results in a failure, and there is no rewarded benefit for being close. Complete perfection, achieved within the stated limits, is absolutely the only thing that is cared about at all.

Granted, getting close might seem just a bit emotionally satisfying, but it doesn’t provide any additional advantage over wildly wrong answers. So, in the cases where perfection doesn’t get achieved, then there is no reason to try to avoid being wildly wrong.

One reason I think my results are nice to be able to see is because I ended up making a bit of a chart. This chart helps to be able to visualize how big the clumps of un-guessed numbers are. I think that this visual presentation can be pleasant, and might even be useful for someone who wishes to contemplate this in hopes of coming up with a better strategy.

Many people probably have the initial inclination to use each available guess to try to split the task into half. I found that approach (Method #1) does not seem to be the approach that maximizes winning. Using Method #1, the sixth guess will often provide the guesser with odds of one in two, or even one in three. However, when using Method #3, the guesser seems to be getting better overall odds of winning. A person could say that the guesser ends up being way more off-track from getting the final answer, because the guesser is left in a situation of being nowhere close to having the final answer in the next guess. However, if the goal is simply to maximize the number of times that correct guesses are made, then Method #3 seems to be the superior approach than starting the first guess at 50. So, as can often be the case in real life, which method seems best may depend on what goals are being pursued.