Odds of completing the "Match" on Monopoly: BONUS CITY?
This is my first post from a longtime lurker. You all are the smartest people when it comes to gaming and odds, so I thought I would *try* to find the answer to my query here. :-D
I am a longtime slot player. I have a YT channel where I show all my slot wins, mainly just for fun. I always like to figure out the odds of "X" happening. I am usually pretty good at it, but this problem has a few things that are stopping me.
Monopoly: BONUS CITY is a popular WMS slot machine. It has a bonus called the "Pick and Match". I want to know the odds of completing it. The idea of the game is to complete property sets before you run out of chances.
All of the famous Monopoly properties are scattered in the match. So there are 6 "three property" matches, and there are 2 "two property" matches (obviously, the Boardwalk/ParkPlace match, and the Baltic/Mediterranean match). In addition, there is one additional "three property set" called the MoneyBags property match.
In sum, there are 7 "three property matches" and 2 "two property" matches. These 25 cards are scattered, face down. The key to the game is you have 7 "spots" to place a card once you select it. Once all 7 spots are taken, the game is over. However, if you get a match by completing ANY property set, the matched properties disappear. For instance, if I select Boardwalk first, it goes down to the Spot 1. If I select Baltic next, it goes to Spot 2. If I select ParkPlace next, it goes to Spot 3, but since it matched, Spots 1 and 3 open up again. Make sense?
What are the odds of completing all the matches before the game ends (when you fill all 7 spots, and there are no matches among the 7)?
The fact that some sets are 3 and others are 2 is confusing me. And I don't know how to implement this "7 spots" thing. or how to make it work, mathematically, by saying if matched, the spots open up again. :-D
Anyone help me? If you can point me in the right direction, I can do all the grunt math. :-D It doesn't matter in what order you match anything, and the Moneybags Match is just 3 MoneyBags. Again, you can match anything in any order.
HELP!! :-D
Brent
Quote: BrentWolgamottHello:
This is my first post from a longtime lurker. You all are the smartest people when it comes to gaming and odds, so I thought I would *try* to find the answer to my query here. :-D
I am a longtime slot player. I have a YT channel where I show all my slot wins, mainly just for fun. I always like to figure out the odds of "X" happening. I am usually pretty good at it, but this problem has a few things that are stopping me.
Monopoly: BONUS CITY is a popular WMS slot machine. It has a bonus called the "Pick and Match". I want to know the odds of completing it. The idea of the game is to complete property sets before you run out of chances.
All of the famous Monopoly properties are scattered in the match. So there are 6 "three property" matches, and there are 2 "two property" matches (obviously, the Boardwalk/ParkPlace match, and the Baltic/Mediterranean match). In addition, there is one additional "three property set" called the MoneyBags property match.
In sum, there are 7 "three property matches" and 2 "two property" matches. These 25 cards are scattered, face down. The key to the game is you have 7 "spots" to place a card once you select it. Once all 7 spots are taken, the game is over. However, if you get a match by completing ANY property set, the matched properties disappear. For instance, if I select Boardwalk first, it goes down to the Spot 1. If I select Baltic next, it goes to Spot 2. If I select ParkPlace next, it goes to Spot 3, but since it matched, Spots 1 and 3 open up again. Make sense?
What are the odds of completing all the matches before the game ends (when you fill all 7 spots, and there are no matches among the 7)?
The fact that some sets are 3 and others are 2 is confusing me. And I don't know how to implement this "7 spots" thing. or how to make it work, mathematically, by saying if matched, the spots open up again. :-D
Anyone help me? If you can point me in the right direction, I can do all the grunt math. :-D It doesn't matter in what order you match anything, and the Moneybags Match is just 3 MoneyBags. Again, you can match anything in any order.
HELP!! :-D
Brent
It's a slot bonus game. The results is probably predetermined.
In other words, the odds are probably not the same as they would be if you were picking random cards.
Quote: AxiomOfChoiceIt's a slot bonus game. The results is probably predetermined.
In other words, the odds are probably not the same as they would be if you were picking random cards.
You could be right, but I generally disagree. Many casino slot games are not predetermined. And if it isn't predetermined, it could be solved. It sounds like a real pain analytically though. :( Simulating it would be a lot easier, I would think.
Quote: tringlomaneYou could be right, but I generally disagree. Many casino slot games are not predetermined. And if it isn't predetermined, it could be solved. It sounds like a real pain analytically though. :( Simulating it would be a lot easier, I would think.
Edit: never mind
Quote: tringlomaneYou could be right, but I generally disagree. Many casino slot games are not predetermined. And if it isn't predetermined, it could be solved. It sounds like a real pain analytically though. :( Simulating it would be a lot easier, I would think.
I did a real quick sim of 1 million trials using php because I'm lazy. Here are my results:
| Two | Three | Total |
|---|---|---|
| 0 | 0 | 762888 |
| 0 | 1 | 73897 |
| 0 | 2 | 8215 |
| 0 | 3 | 1146 |
| 0 | 4 | 135 |
| 1 | 0 | 110020 |
| 1 | 1 | 23827 |
| 1 | 2 | 5050 |
| 1 | 3 | 1146 |
| 1 | 4 | 186 |
| 2 | 0 | 7129 |
| 2 | 1 | 3140 |
| 2 | 2 | 1223 |
| 2 | 3 | 416 |
| 2 | 7 | 1582 |
Looks like 1 in about every 624 attempts.
No matches in 76.3% of attempts? Ouch.
Brent, if you play this a lot, does roughly 75% of bonus rounds no matches sound reasonable? If it happened to you much, much less: say 25% of the time, then it could be predetermined like Axiom suggested.
Quote: tringlomaneThanks miplet. :)
No matches in 76.3% of attempts? Ouch.
Brent, if you play this a lot, does roughly 75% of bonus rounds no matches sound reasonable? If it happened to you much, much less: say 25% of the time, then it could be predetermined like Axiom suggested.
miplet,
As you know, I don't have the math chops to disagree with your numbers. But I'm finding the "no matches" situation @76% almost impossible to accept; after all, it's a bonus round, might take hundreds of spins just to get to try. Maybe each property has a value when it's picked and you get some minor amount added to your win as you pick each card? (Not that you're the OP). So you get a minor bonus payout even if you match none.
The other thing is, it should get progressively easier to get a really big score as you go along; the first hurdle is the hardest, but once you get the first group of 3, you have the same 7 spots, (with 3 freshly freed up) and only 6 groups of 3 to match from, so your odds have improved. As they would continue to do throughout the game; the next group each time would leave the same 7 spots but progressively less "wrong" choices. If, for example, you managed to get 6 of the 3-property groups, you automatically get all 9, right? 2+2+3 is all that's left. I think.
I could be wrong. Easily.
Quote: miplethttp://youtu.be/pFSyEB3J2kc
I kind of want to play this now. I am such a sucker.
Quote: beachbumbabsmiplet,
As you know, I don't have the math chops to disagree with your numbers. But I'm finding the "no matches" situation @76% almost impossible to accept; after all, it's a bonus round, might take hundreds of spins just to get to try. Maybe each property has a value when it's picked and you get some minor amount added to your win as you pick each card? (Not that you're the OP). So you get a minor bonus payout even if you match none.
No, it's acceptable because as you correctly guessed, you get credits for every pick made. There are plenty of other slot bonus games that end in less than 7 selections too. Looks like dark purple/brown properties get 0.5X total bet, orange 2X total bet, red 2.5X total bet, green 4X total bet, money bag (variable: 2.5X to 25X total bet). I dunno about the rest because he didn't get a group match, but he still won 25X bet total in the bonus. I would guess light blue is 1X, light purple 1.5X, Yellow 3X, Blue 5X? Extra bonuses for a property group match? Maybe Brent can answer that one.
As for 75% of the time being "no matches"....that doesn't sound unreasonable. Many times I have gone through it and not matched at all. The thing to keep in mind is: if you trigger the bonus on more than one line (there are 40 lines), then you get double or even triple whatever you earned. So it's not like you don't win a fair amount, even if you go "7 and out". :-D
Also, keep in mind the video above, the player got a 'Big win' (more than 20x) and he didn't get ONE match. :-D
Thank you guys so much for doing this. I don't know enough about probability in THIS area to know if your math is right, but it doesn't seem at all unreasonable, so I accept it. :-D
EDIT to add: Here is an example of someone triggering on more than one line. They actually only matched once, and the crappiest properties at that, but they got a nice 70x their win":
