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Both Invisible Castle and RPOL.NET function with the above information in mind, however, RPOL.NET can be used to create a game and assign characters to people who join, allowing you to keep track of the die rolls of individual players. All the results are tamper proof.
Custom-made to answer this question: RollDB RollDB is a PHP-based web application that connects to a SQL database (quasi-)permanently storing roll results in both text and number format. You can specify an ID beforehand, or have one assigned at random. Right now it supports a number of common rolls for Shadowrun, the d6 System, the d20 System, Fate, and ...
Use any hashing algorithm and you don't need to trust the randomness algorithm of a website and you can verify the randomness yourself. Heres an example using MD5, but any reasonable hash algo will work. You can use any program online to do MD5, like http://www.miraclesalad.com/webtools/md5.php Say I want to roll a 6 sided die I send you MD5("1337") ...
The older solution is dice server that emails the die rolls to both parties. http://www.cyrnus.com/cgi-bin/rollem.cgi http://dicelog.com/dice http://www.pbm.com/dice/
Invisible Castle works well for this, with the saving of rolls to a character's profile and inability to delete them, but if you're really worried about players cheating, my preference is Hamate aka Dicelog. You can have the player email the roll to you - the email comes from dicelog as soon as he makes the roll, with his note about what roll it is, etc ...
The website Invisible Castle has this exact functionality, and with this exact purpose in mind. It saves the rolls with tags for character, campaign, etc. You can look up the entire roll history of a player, such as this test user.
Giant in the Playground’s roller is tamper-resistant; any edit to the roll-code after posting, and the post gets a big red angry message and it messes up the roll. But the real solution, of course, is trusting your players. If you cannot trust your players, you don’t have a game, and no amount of anti-cheat device will fix that. You need to fix ...
From your question, I imagine you need this to a play-by-forum game, and wouldn't be online at the same time than the player. If you CAN be online at the same time than the player, just go to Rolz, create a room a you're done. If you can't, just go to Rolz anyway, create a room and you're done. Rolz save all the logs from rolls, so you can make your ...
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