The Math Behind Roobet's Mines | Crypto Casino Game Odds

[00:01] over a game that a lot of you have been requesting and that's the mindes game on ret.com we'll be going over the basics of the game as well as the math to calculate the expected returns while playing first of all let's give a quick

[00:13] overview of how the game is played the player starts off with 25 spaces on the 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

[00:27] 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

[00:40] the board and the amount of spaces that you uncover for example if there's a it after five turns you can cash out for 1.21 times your bet however if there are three bombs hidden on the board and you

[00:53] successfully uncover five tiles you can now cash out for 1.96 times your original bet since it's more difficult to dodge a large L amount of bombs if the player does uncover a space with the bomb the game is immediately over and

[01:05] payout is different depending on the number of hidden bombs and the number of tiles uncovered we need the formula that rubet uses to calculate the multiplier couldn't find this formula anywhere in the code that they provide so I reached

[01:20] making a video about mines and I asked for this calculation so that I can inform my viewers about the expected value of the game they responded with unfortunately that is not information that we could provide in my opinion it's

[01:34] 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 informed while making decisions on their site which I think we all know the

[01:47] answer to it's been over 2 months and they still haven't responded so that 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

[02:00] that were cleared and the payout multiplier The Next Step was to find the 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

[02:15] 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

[02:28] first pick there are not 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 the next two tiles that we need to uncover and after multiplying these

[02:43] 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% and this calculation can also be simplified to this formula here using factorials then

[02:57] and I found 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

[03:11] $1 on this game we found that we would expect to win this bet 70% of the time and each time we win we would profit 39 the other 30% of the time we would lose our $1 this comes out to an expected value of -2.7 cents per play or -

[03:26] 2.7% so this is great when we know the multiplier of a certain situation but possible combination of bombs on the board and spaces cleared is nearly impossible for example the probability of successfully clearing 12 spaces when

[03:40] of successfully clearing 12 spaces when there's 13 bombs on the board is there's 13 bombs on the board is 0.19% or just about 1 in 5.2 million so every possible scenario by playing ourselves we still need to figure out

[03:52] what function they're using to calculate the payout for each game situation now I did manually collect the multipliers for 7 6 out of the 300 possible game situations and I calculated the expected value for each one here's what the

[04:05] distribution of these expected values looks like first of all we can see that all these bets have a negative expected value but some have expected values that are worse than others they range from NE 3.4% to - 2.7% and seem to be centered

[04:20] at just around -3% now if a bet is fair and has an should be one 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

[04:34] bet because I saw that this distribution of expected values was centered at around -3% I calculated what the multipliers should be if they were even bets and then I subtracted 3% which is the same thing as multiplying by 97 then

[04:47] two decimal places since that's how precise the multipliers are in the mindes game and after comparing the multipliers from this calculation to the 76 multipliers that we actually knew we could see that they exactly so we can be

[05:01] formula that rubet is using and now calculate the expected multipliers for all of the 300 possible game situations that has the highest win percentage but lowest multiplier is when you uncover

[05:16] one space when there's a single bomb on the board this bet has a success rate of the board this bet has a success rate of 96% a multiplier of 1.01 and an expected value of 3.04% there are two bets that are tied

[05:28] 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

[05:40] of these situations have a success rate of 0.19% they have expected multipliers of 5,442 19.95 and expected values of

[05:52] -3% however the minimum bet on mines is 1 cent and the maximum win amount on one game is capped at $20,000 so you wouldn't even be able to cash out the full $50,000 that you should have after winning this bet with even 1 cent now

[06:06] let's look at the bets with the lowest and highest expected values there are best expected value these are the situations when you have two bombs on spaces and also when you have four bombs on the board and have to remove two

[06:20] spaces these scenarios both have success rates of 70% multipliers of 1.39 and expected values of - 2.7% there are four bets that are tied for having the worst expected value these are the situations when you have

[06:34] 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

[06:47] values of - 3.4% I know it wouldn't be fun to use the formula every time you want to know the multiplier or the expected value of easier recently I've been wanting to

[06:59] figured that this project could be a great opportunity to do that I created a 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

[07:13] you the probability of successfully winning the bet for example let's say want to clear three spaces after we we're told that the predicted multiplier is 4.9 we have a 19.78% chance of

[07:27] winning and we expect to lose 3. 07 for every $1 that we bet I'll leave a link to check the site out just keep in mind that rubet can change their multiplier possible that these estimations of the multiplier and expected values aren't

[07:43] 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'd really help me out YouTube will show it to more people thanks again for watching and I'll see

[07:55] thanks again for watching and I'll see you in the next video