Best way to split costs during travelling

I've always used your option number 3. It's not difficult to figure out how much every one has paid!

Take a notebook with you in your trip. Draw 4 columns, the first one for item names you must pay in common (transport, accommodation...) and the other 3 columns for the amount each person paid for each item.

For example, if Person 1 pay $10 a taxi, you write in the first column "Taxi from A to B" and the amount 10 under the column for Person 1. If Person 1 and Person 2 pay $30 each one for a Hotel, you'll write "Hotel at X" and 30 under Person 1 and Person 2.

Item         |   Person 1   |  Person 2  |   Person 3
-----------------------------------------------------
Taxi A to B  |     10       |            |
Hotel at X   |     30       |    30      |

When you finish your trip, sum up the 3 columns. It will give you the amount paid for each people. Sum up these 3 values and divide by 3 (mean) and you have the balance each one has to pay to others.

For example, Person 1 has a sum of 100, Person 2 has a sum of 120 and Person 3 has a sum of 80. The mean is (100 + 120 + 80) / 3 = 100. So Person 1 is ok because he/she has paid exactly the mean; Person 2 is 120 - 100 = 20 over the mean so he/she must get $20 from Person 3 that is 80 - 100 = -20, $20 under the mean.

Item         |   Person 1   |  Person 2  |   Person 3
-----------------------------------------------------
Taxi A to B  |     10       |            |
Hotel at X   |     30       |    30      |
 ........    |    ....      |   ....     |
-----------------------------------------------------
                  100            120           80
 Mean        |       (100 + 120 + 80) / 3 = 100
 Diff        |     0        |     20     |    -20

This way each person can pay with their own credit card and it's easy to know how much is the balance to pay each other.

HACK: If you make the sum up in the middle of the trip you can know who's under the mean and then use this information to decide who's the next people who must pay.

I've always used option 2: make a pot of cash in which everyone puts the same amount. Then use the money from that pot to pay for common costs - food, accommodation, petrol, etc. If you are worried about carrying a lot of cash you can make the pot as small as you feel comfortable with, and simply refill it more often. 50€ per person is a good start in my opinion. This might come with the drawback of increased cost due to the commissions on a larger number of cash withdrawals, depending on your bank and country of travel.

A more advanced version of the pot could be a dedicated bank account with a linked payment card. It doesn't have to be a joint account within all the travellers. Rather it would make more sense for the person with the best banking deals to open it, and be the guardian of the pot. Come to think of it, this is what I will do next time I travel.

Personally I hate calculating who paid what with scientific hundredths precision. Hence why I prefer the pot method.

If you own a "Smartphone" you could use an App as such: http://tricount.com/en/mobiles/ .

It enable to log who pays what. Each travler old its own money and pays at his turn (that avoid non-trush to other problems). You can record who profit from the expense if one is missing. At the end you do the balance that is computed by the application.

We did it couple of time with friends and it work great! Event with a group of 10 peoples.

Me and my friends faced issues like this for long long time. Previously, we used to calculate amount on paper which wasn't hard but tedious. Because, in a group of people more than 2 there might be some chances that Person 1 and Person 2 are only included in a transaction and for that particular transaction Person 3 should not be charged. Then, we start using BillsAreIn which has a nice mechanism for bill sharing and has awesome feature like I.O.U. [I Owe You]. It will also give you complete statistic of items/things on which you are spending more. Again, you can divide a bill among relative partners.

As it requires internet connectivity, which usually we don't have it while travelling so we use to track it down on a paper and whenever we get internet we update our bills.

Disclaimer: I am nowhere related to this site & do not hold any responsibility of it functionality. I have just recommend it based on my personal experience. For more information see the website's tour.

If the phones aren't an issue, SplitWise (which others have suggested) does work offline to some degree. It might be easier than jotting everything down. Obviously, the major point here is whether or not you'll even have a phone at your disposal.