My niece and I are working on a project to calculate the probability of the first player, reaching boardwalk space. Oh we are using the US version of the game.

By our figuring the only way to do this is to land on a chance and draw the "go to boardwalk card".

So we have tried to describe every way of landing on chance (and drawing the card). Here is what we have so far:

• roll a 7(any), then draw go to boardwalk card from chance
• roll 2(1,1), then roll 5(any), then draw go to boardwalk card from chance
• roll 4(2,2), then roll 3(any), then draw go to boardwalk card from chance
• roll 12(6,6), then roll 10(any), then draw go to boardwalk card from chance
• roll 10(5,5), then roll 12(6,6), then draw go to boardwalk card from chance
• roll 2(1,1), draw "go to go" (from community chest), roll 7(any), then draw go to boardwalk card from chance

We really aren't looking for help calculating the probability of the above situations. We are interested if anyone can think of a way we have missed to get to boardwalk. Thanks!

Looks good so far. Are you not including the possibility of rolling doubles twice, then rolling a third time and landing on chance? (If I remember correctly, you can roll a third time in a row as long as doubles aren't rolled again)

three more:

• roll 2(1,1), draw "go to go", roll 2(1,1), then roll 5(any), then draw go to boardwalk card from chance
• roll 2(1,1), draw "go to go", roll 4(2,2), then roll 3(any), then draw go to boardwalk card from chance
• roll 2(1,1), roll 2(1,1), roll 3(any), then draw go to boardwalk card from chance

yeah i think i incorporated what you suggested in my last post; let me know if you see anymore

It's been forever since I played, where are the "Advance to St. Charles Place"/ "Take a ride on the Reading Railroad"/ etc. cards located?
If those can be used, it can get pretty hectic

i looked at those and I'm of the opinion they are not helpful for getting to boardwalk. The logic being, is that chance #7 is an odd number, so you can't get to it with a double, meaning your turn will end when you get moved by the card (so it better take you to boardwalk).

recapping what I got so far:

All cases the final step is landing on chance and drawing "go to boardwalk card":

using chance #7
roll 7(any)
roll 4(2,2), roll 3(any)
roll 2(1,1)(not draw go to go), roll 5(any)
roll 2(1,1)(not draw go to go), roll 2(1,1), roll 3(any)


using community chest #2 + chance #7
roll 2(1,1)(draw "go to go"), roll 7(any)
roll 2(1,1)(draw "go to go"), roll 2(1,1), roll 5(any)
roll 2(1,1)(draw "go to go"), roll 4(2,2), roll 3(any)


using chance #22
roll 12(6,6), roll 10(any)
roll 12(6,6), roll 6(3,3), roll 4(non-double)
roll 12(6,6), roll 4(2,2), roll 6(non-double)
roll 12(6,6), roll 2(1,1), roll 8(non-double)

roll 10(5,5), roll 12(6,6)
roll 10(5,5), roll 8(4,4), roll 4(non-double)
roll 10(5,5), roll 6(3,3), roll 6(non-double)
roll 10(5,5), roll 4(2,2), roll 8(non-double)
roll 10(5,5), roll 2(1,1), roll 10(non-double)

roll 8(4,4), roll 10(5,5), roll 4(non-double)
roll 8(4,4), roll 8(4,4), roll 6(non-double)
roll 8(4,4), roll 6(3,3), roll 8(non-double)
roll 8(4,4), roll 4(2,2), roll 10(non-double)

roll 6(3,3), roll 12(6,6), roll 4(non-double)
roll 6(3,3), roll 10(5,5), roll 6(non-double)
roll 6(3,3), roll 8(4,4), roll 8(non-double)
roll 6(3,3), roll 6(3,3), roll 10(non-double)

roll 4(2,2), roll 12(6,6), roll 6(non-double)
roll 4(2,2), roll 10(5,5), roll 8(non-double)
roll 4(2,2), roll 8(4,4), roll 10(non-double)

roll 2(1,1)(not draw go to go), roll 12(6,6), roll 8(non-double)
roll 2(1,1)(not draw go to go), roll 10(5,5), roll 10(non-double)

update:
this is turning out to be much more complicated than I thought it would, I was expecting 3-8 ways at most!

using chance #7; using go to boardwalk card on final step
roll 7(any)
roll 4(2,2), roll 3(any)
roll 2(1,1)(not draw go to go), roll 5(any)
roll 2(1,1)(not draw go to go), roll 2(1,1), roll 3(any)


using community chest #2 + chance #7; using go to boardwalk card on final step
roll 2(1,1)(draw "go to go"), roll 7(any)
roll 2(1,1)(draw "go to go"), roll 2(1,1), roll 5(any)
roll 2(1,1)(draw "go to go"), roll 4(2,2), roll 3(any)


using chance #22; using go to boardwalk on final step
roll 12(6,6), roll 10(any)
roll 12(6,6), roll 6(3,3), roll 4(non-double)
roll 12(6,6), roll 4(2,2), roll 6(non-double)
roll 12(6,6), roll 2(1,1), roll 8(non-double)

roll 10(5,5), roll 12(6,6)
roll 10(5,5), roll 8(4,4), roll 4(non-double)
roll 10(5,5), roll 6(3,3), roll 6(non-double)
roll 10(5,5), roll 4(2,2), roll 8(non-double)
roll 10(5,5), roll 2(1,1), roll 10(non-double)

roll 8(4,4), roll 10(5,5), roll 4(non-double)
roll 8(4,4), roll 8(4,4), roll 6(non-double)
roll 8(4,4), roll 6(3,3), roll 8(non-double)
roll 8(4,4), roll 4(2,2), roll 10(non-double)

roll 6(3,3), roll 12(6,6), roll 4(non-double)
roll 6(3,3), roll 10(5,5), roll 6(non-double)
roll 6(3,3), roll 8(4,4), roll 8(non-double)
roll 6(3,3), roll 6(3,3), roll 10(non-double)

roll 4(2,2), roll 12(6,6), roll 6(non-double)
roll 4(2,2), roll 10(5,5), roll 8(non-double)
roll 4(2,2), roll 8(4,4), roll 10(non-double)

roll 2(1,1)(not draw go to go), roll 12(6,6), roll 8(non-double)
roll 2(1,1)(not draw go to go), roll 10(5,5), roll 10(non-double)
roll 2(1,1)(draw go to go), roll 12(6,6), roll 10(non-double)


using chance #22 NOT using boardwalk on final step
roll 12(6,6), roll 10(5,5)(draw go to nearest utility), roll 11(any)(land on boardwalk)
roll 10(5,5), roll 12(6,6)(draw go to nearest utility), roll 11(any)(land on boardwalk)

eventually wrote program to bruteforce all possible outcomes of a turn, the final answer is about 1.1%

Found a few more... you can roll 22 in your first two turns, hit the goto utility card, then make it to the last chance... then pull the goto board walk card.

You can customize the rules. A lot of times you do go directly to jail when doubles are rolled three times in a row.
We place any payments that doesn't go to another player into the free parking space. Easy money if you land there.

This post was edited by Madmartigan on Feb 11 2014 10:57pm