04.05.2024

In today's video we're going to be going. over a game that a lot of you have been. requesting and that's the minds game on. rubette.com. we'll be going over the basics of the. game as well as the math that calculate. the expected returns while playing. first of all let's give a quick overview. of how the game is played the player. starts off with 25 spaces on the board. and gets to choose the number of bombs. that are hidden under these spaces you. can have a single bomb on the board or. you can have up to 24 bombs leaving only. a single empty space. at this point you also decide on the. amount that you'd like to bet on the. game the player then has a chance to. uncover these spaces one at a time if. they successfully Dodge a bomb a. multiplier appears on the space and the. player is allowed to cash out for that.

Amount this multiplier changes based on. the number of bombs that are on the. board and the amount of spaces that you. uncover for example if there's a single. bomb on the board and you dodge it after. five turns you can cash out for 1.21. times your bet. however if there are three bumps hidden. on the board and you successfully. uncover 5 tiles you can now cash out for. 1.96 times your original bet since it's. more difficult to dodge a larger amount. of bombs if the player does uncover a. space with a bomb the game is. immediately over and they lose their. entire bet. because the payout is different. depending on the number of hidden bombs. and the number of tiles uncovered we. need the formula that rubat uses to. calculate the multiplier. after searching on their website I. couldn't find this formula anywhere in.

The code that they provide so I reached. out to rubette explaining that I was. making a video about mines and I asked. for this calculation so that I could. inform my viewers about the expected. value of the game. they responded with the following. message stating unfortunately that is. not information that we could provide in. my opinion it's ridiculous that the. players don't get to know what their. payout will be before taking the risk of. uncovering another tile. I responded with another email giving my. opinion and asking why they don't want. their users to be better informed while. making decisions on their site which I. think we all know the answer to it's. been over two months and they still. haven't responded. so that means that we're gonna have to. figure out how they calculate the. multiplier on our own.

The first thing that I did was collect. some data I tested out different. scenarios and recorded the number of. bombs on the board the number of spaces. that were cleared and the payout. multiplier. The Next Step was to find the. probability of uncovering a given number. of spaces with a certain amount of bombs. on the board we'll look at a specific. example to show how we'd calculate this. let's say we want to find the. probability of clearing four spaces when. there's two bombs on the board since. there's 25 spaces total and the two. bombs are randomly placed the chance. that we uncover a safe tile on our first. pick is 23 out of 25. assuming that we. successfully missed the bomb on the. first pick there are now two bombs and. 22 safe tiles out of 24 spaces so our. probability of dodging a bomb on the. second pick is now 22 out of 24. we can.

Find similar probabilities for each of. the next two tiles that we need to. uncover and after multiplying these. fractions together we get the overall. probability of dodging a bomb after. uncovering four tiles in this case the. probability turns out to be 70 percent. and this calculation can also be. simplified to this formula here using. factorials then I actually played the. scenario on mines and I found out that. the multiplier for clearing four spaces. with two bombs on the board turns out to. be 1.39. and now that we have the multiplier we. can calculate the expected value of this. specific bet let's say that we bet one. dollar on this game we found that we. would expect to win this bet 70 percent. of the time and each time we win we. would profit 39 cents the other thirty. percent of the time we would lose our.

One dollar this comes out to an expected. value of negative 2.7 cents per play or. negative 2.7 percent. so this is great when we know the. multiplier of a certain situation but. finding this multiplier for every. possible combination of bombs on the. board and space is cleared is nearly. impossible. for example the probability of. successfully clearing 12 spaces when. there's 13 bombs on the board is point. zero zero zero zero one nine percent or. just about one in 5.2 million so we. can't just find the multiplier for every. possible scenario by playing ourselves. we still need to figure out what. function they're using to calculate the. payout for each game situation now I did. manually collect the multipliers for 76. out of the 300 possible game situations. and I calculated the expected value for. each one here's what the distribution of.

These expected values looks like. first of all we can see that all these. bats have a negative expected value but. some have expected values that are worse. than others they range from negative 3.4. percent to negative 2.7 percent and seem. to be centered at just around negative. three percent. now if a bet is fair and has an expected. value of zero the multiplier should be 1. over the probability of winning. for example the multiplier for a bet. that you have a 50 chance of winning. should be two if it's an even bet. because I saw that this distribution of. expected values was centered at around. negative three percent I calculated what. the multiplier should be if they were. even bets and then I subtracted three. percent which is the same thing as. multiplying by 0.97. then I rounded each of these multipliers.

To two decimal places since that's how. precise the multipliers are in the mines. game. and after comparing the multipliers from. this calculation to the 76 multipliers. that we actually knew we could see that. they matched exactly so we can be pretty. confident that this is the formula that. Ruben is using and now we're able to use. this formula to calculate the expected. multipliers for all of the 300 possible. game situations after doing this we can. see that the bet that has the highest. win percentage but lowest multiplier is. when you uncover one space when there's. a single bomb on the board this bet has. a success rate of 96 percent a. multiplier of 1.01 and an expected value. of negative 3.04 percent there are two. bets that are tied for the lowest win. percentage but the highest multiplier. this is when you have 13 bombs on the.

Board and need to uncover 12 spaces or. when there's 12 bombs on the board and. you need to uncover 13 spaces as we saw. earlier both of these situations have a. success rate of. 0.000019 percent they have expected. multipliers of 5 million 44. 290.95 and expected values of negative. three percent. however the minimum bet on mines is one. cent and the maximum win amount on one. game is capped at twenty thousand. dollars so you wouldn't even be able to. cash out the full fifty thousand dollars. that you should have after winning this. bet with even one cent. now let's look at the bets with the. lowest and highest expected values. there are two beds that are tied for. having the best expected value these are. the situations when you have two bombs. on the board and you have to remove four. spaces and also when you have four bombs.

On the board and have to remove two. spaces these scenarios both have success. rates of seventy percent multipliers of. 1.39 and expected values of negative 2.7. percent. there are four bets that are tied for. having the worst expected value these. are the situations when you have four. bombs on the board and have to remove. one space when you have one bomb on the. board and need to remove four spaces two. bombs on the board and need to remove. one space and one bomb on the board when. you need to remove two spaces. all four of these bets have expected. values of negative 3.4 percent. I know it wouldn't be fun to use the. formula every time you want to know the. multiplier or the expected value of a. bet so I try to make things a bit easier. recently I've been wanting to learn how. to create a web app and I figured that.

This project could be a great. opportunity to do that I created a. website where you can put in the number. of bombs on the board and the number of. spaces cleared to calculate the. predicted multiplier and expected value. of the bet. the calculator will also tell you the. probability of successfully winning the. bet. for example let's say there's 10 bombs. on the board and we want to clear three. spaces after we enter these values and. press calculate we're told that the. predicted multiplier is 4.9 we have a. 19.78 chance of winning and we expect to. lose 3.07 cents for every one dollar. that we bet I'll leave a link in the. video description if you'd like to check. the site out just keep in mind that. rubette can change their multiplier. calculation at any point so it's. possible that these estimations of the.

multiplier and expected values aren't. completely accurate thanks for watching. the video and be sure to leave a comment. if you have any topics that you'd like. me to cover. also it really helped me out if you left. a like on the video so that YouTube will. show it to more people. thanks again for watching and I'll see. you in the next video. foreign