Ever since we have purchased the Monopoly board game, it has become a weekend ritual for us. Almost every Friday/Saturday night Jo would pull out the board, currency, wooden dice, small houses and deed cards and spread them.
We are in for a surprise after playing the game for few weeks. As kids we thought the game is a GAME, ie random to high extent but fun. But as we develop an eye for the detail, the game does come out to be rather unfair. How else can you explain that one of us is paying rents through their noses to the other one owning reds and oranges and how else can you explain that the one who purchased properties next to GO seldom gets a visitor, including themselves. We started questioning, is monopoly fair? And thats where I set out to find it myself.
For starters, The monopoly board has 40 cells, and every player starts at GO. The moves are decided by sum of the faces on a 2 dice throw. If you get a double you get to throw again.
I have tried to simulate the game using excel. I have observed all the rules like community chest / chance cards, Jail and go to jail. But I have not observed doubles rule for I thought it had little impact on the outcome. I wanted to see if the expected probabilities of each cell (which is 1/40 or 2.5%) are close to the actual probabilities.
When I ran the simulation for 10000 dice throws for 4 players, the absolute difference between expected probabilities of each cell, color group are more or less near to the actual probabilities as you can see in the below charts. (click on them for bigger versions)
The maximum deviation is to the tune of 6% for individual cells and 1.93% for a color group (for there will be cancellations in color groups, as one cell gets more visitors the other would get less)
But that is not we experience when we play the game. We end up landing in Jail or a chance an awful lot of times more than we expect to land there. Thats because, no one ever plays a 10000 throw per person game, not in day to day versions. Its more like 200-400 throws. So when I ran the same experiment for 200 turns for 4 players, the results were more interesting as you can see them below.
As you can see the deviation in the actual probability and expected probability is huge. Some times 60% more for individual cells and 20% for color groups. This I guess explains the reason behind the Monopoly game strategies like buy anything in Orange and Red groups etc.
Obviously one fault of this experiment is if you run it again the actual probabilities are going to change in favor of something else. But almost always far from the expected results.
Write to me just in case you want to play around with my monopoly board game simulation excel sheet, I can mail it. The file is rather huge for upload.
Related links: Monopoly Wiki, Monopoly Fun Facts & Strategies, Similar Monopoly Simulations [1, 2]
15 Responses to “Christmas Gift List – Set your budget and track gifts using Excel”
[...] Christmas Gift List – Set your budget and track gifts using Excel … [...]
I'm confused: if you spend $10, and your budget is $40, shouldn't the amount in the "Within Budget?" column stay black, since you didn't go over budget?
In other words, since we overspent on the electronic photo frame, shouldn't the $8 cell turn red?
@JP.. maybe Steven is encouraging consumerism... ?
I havent realized it earlier, but now I see it. If you unprotect the sheet, you can change the formula in Column I to =IF(G13=0;" ";F13-G13) from =IF(G13=0;" ";G13-F13), that should correct the behavior.
Thanks Chandoo. I thought of making a shopping list spreadsheet for Christmas, but this is neat so I think I'll use this instead.
Chandoo & Steven thanks for this spreadsheet. But for the sake of a person who has been staring at this megaformula in vain for the last 40 mins and not afraid to ask, would it be possible for you to walk us through the logic used here?
=SUM(SUMPRODUCT(SUBTOTAL(3,OFFSET($K$13:$K$62,ROW($K$13:$K$62)-MIN(ROW($K$13:$K$62)),0,1)),--($K$13:$K$62="-"))+SUMPRODUCT(SUBTOTAL(3,OFFSET($K$13:$K$62,ROW($K$13:$K$62)-MIN(ROW($K$13:$K$62)),0,1)),--($K$13:$K$62="0")))&" / "&SUBTOTAL(2,$G$13:$G$62)
Thanks Chandoo.. This is one of the best budget spreadsheets I've ever seen.. The Arrays are out of this world!! And it's FREE!!
Chandoo, can you tell us more about Steven? Does he have his own site?
JP, I think Chandoo changed it when he changed the currency formatting from £ to $, a negative figure is a good thing in this case. But don't change the formulas, the overbudget and under budget won't work properly if you do. Also Chandoo I think you've accidentally broke the conditional formatting for the alternating row colouring the formula is different to the version I sent you. As for the megaformula chrisham, it gave me a headache trying to get it all working, so I will let Chandoo talk you through it.
Hi,
In cells I6 and I7, I understand that subtotal together with offset function returns an array of ones after which, the sumproduct function gives the desired result.
But I’m not able to figure out the reason for using an array in I8 to return the most expensive gift.
Can’t the formula be just
“=VLOOKUP(SUBTOTAL(4,$G$13:$G$62),$G$13:$J$62,4,0)”
Savithri, Cell I8 needs the array, if the formula was “=VLOOKUP(SUBTOTAL(4,$G$13:$G$62),$G$13:$J$62,4,0)” it would find the highest price from the filtered range (i.e. highest actual in filtered range is $50) BUT then return the first person with that actual, not looking in just the filtered range (so first person on the list with a $50 actual.)
To see what I mean, change the formula, then change all the actuals to $50 then filter for baby, it lists the first name on the list.
But a good question 🙂
Thank you. I now realise that the array is used to get the ‘filtered range’ instead of the entire range, as table array for look up value.
[...] Download This Template [...]
this looks like an awesome excel sheet!! is there anyway i can get it emailed to me unprotected? for some reason, i am unable to download it 🙁 help!!
Hi I also can not download to a mac as the sheet is protected any help would be great
[...] to send her a pricey present. Rather, send a card with a picture of your child. Here’s a cool Excel sheet that will help you estimate your budget per person and let you track [...]
[...] husband and I pour/poor over the Christmas spreadsheet (yes, I do know how dorky that sounds, but we’re not the only ones!), figuring out who should give what to whom. We live at a distance from most of our family, so it [...]