I'm sticking with my second method, which got me 59.68 (truncated to 2 decimal places, not rounded) If I had rounded it would have been 59.69, which it probably should be, but it's the mehtod I care about anyway, which I now believe is correct, for whatever that's worth.
"Well sure, the FrinkiacVII looks impressive - DON'T TOUCH IT - but I predict that within 100 years computers will be TWICE as powerful, ten THOUSAND times larger, and so expensive that only the five richest kings of Europe will own them." -Prof. Frink
I'm sticking with my second method, which got me 59.68 (truncated to 2 decimal places, not rounded) If I had rounded it would have been 59.69, which it probably should be, but it's the mehtod I care about anyway, which I now believe is correct, for whatever that's worth.
The great thing about math is that you can often check your answers by alternate methods. You used one method and I used another.
The method I used is labourous but works well (and is easy to visualise) - however only for a small number of 'rolls'. 5 rolls is really the limit I would normally consider simply because drawing up large tables is impractical and prone to error.
Spreadsheets help - but it's easy to get blinded by a page full of numbers. Use of Colour is a very big help in this case to and can help spot patterns and mistakes.
For bigger problems - I would (and do) use your method. Sometimes you can also work problems by working out the chance that an event does not happen to calculate the chance that it does. I always check that my probabilities add up to 1 to make sure I have covered everything - this is where I find errors most of the time... and AnthonyGrey: the fact that you have 63 possible outcomes tells you something is wrong straight away.
Overkillengine used the Monte Carlo method which is also quite valid - provided you do enough rolls. This method is very popular now with computers being able to rapidly process large amounts of data. But personally, I only use it as a last resort simply because it may not show you all possibilities when dealing with complex systems like RPGs and player choices (which are not always either random or logical!)
Monte Carlo method is also done by playtesting - and this is why I believe Games Workshop so often get it wrong. When dealing with very complex rulesets (most GW games) a couple of games to "playtest" is simply not enough. You need to follow rulesets through and find the possible extremes.
The method I used is labourous but works well (and is easy to visualise) - however only for a small number of 'rolls'. 5 rolls is really the limit I would normally consider simply because drawing up large tables is impractical and prone to error.
Spreadsheets help - but it's easy to get blinded by a page full of numbers. Use of Colour is a very big help in this case to and can help spot patterns and mistakes.
Nonsense. Excel complains if you go over 2^24 (approximately 17 million) cells in use (at least Excel 2007 does; I'm not sure about newer versions), but 1 million or so cells is easy. Make the formulas for one line, then copy and paste to a hundred lines. Or a thousand. Or ten thousand. Or, if you needed few enough cells per line, 1048576 lines by using Ctrl+arrow key.
And if that's not enough, change one unused value to reroll all of the random number generators and get a new trial with however much data you had before.
The method I used is labourous but works well (and is easy to visualise) - however only for a small number of 'rolls'. 5 rolls is really the limit I would normally consider simply because drawing up large tables is impractical and prone to error.
Spreadsheets help - but it's easy to get blinded by a page full of numbers. Use of Colour is a very big help in this case to and can help spot patterns and mistakes.
Nonsense. Excel complains if you go over 2^24 (approximately 17 million) cells in use (at least Excel 2007 does; I'm not sure about newer versions), but 1 million or so cells is easy. Make the formulas for one line, then copy and paste to a hundred lines. Or a thousand. Or ten thousand. Or, if you needed few enough cells per line, 1048576 lines by using Ctrl+arrow key.
And if that's not enough, change one unused value to reroll all of the random number generators and get a new trial with however much data you had before.
I'm not sure if you are just disagreeing with me for the sake of it now?
I did say that spreadsheets help (particularly with the use of colour) but what you appear to be describing is not a matrix like I drew - but a method of doing a Monte Carlo exactly as Overkillengine did.
I'm fine with Monte Carlos in the right applications (I used to be a Blackjack player and studied the game extensively - many BJ analysis are based on Monte Carlo runs) but it's not always appropriate in my view.
It's sometimes really handy to be able to compare odds as fractions for example.
Comments
I'm sticking with my second method, which got me 59.68 (truncated to 2 decimal places, not rounded) If I had rounded it would have been 59.69, which it probably should be, but it's the mehtod I care about anyway, which I now believe is correct, for whatever that's worth.
"Well sure, the FrinkiacVII looks impressive - DON'T TOUCH IT - but I predict that within 100 years computers will be TWICE as powerful, ten THOUSAND times larger, and so expensive that only the five richest kings of Europe will own them." -Prof. Frink
The great thing about math is that you can often check your answers by alternate methods. You used one method and I used another.
The method I used is labourous but works well (and is easy to visualise) - however only for a small number of 'rolls'. 5 rolls is really the limit I would normally consider simply because drawing up large tables is impractical and prone to error.
Spreadsheets help - but it's easy to get blinded by a page full of numbers. Use of Colour is a very big help in this case to and can help spot patterns and mistakes.
For bigger problems - I would (and do) use your method. Sometimes you can also work problems by working out the chance that an event does not happen to calculate the chance that it does. I always check that my probabilities add up to 1 to make sure I have covered everything - this is where I find errors most of the time... and AnthonyGrey: the fact that you have 63 possible outcomes tells you something is wrong straight away.
Overkillengine used the Monte Carlo method which is also quite valid - provided you do enough rolls. This method is very popular now with computers being able to rapidly process large amounts of data. But personally, I only use it as a last resort simply because it may not show you all possibilities when dealing with complex systems like RPGs and player choices (which are not always either random or logical!)
Monte Carlo method is also done by playtesting - and this is why I believe Games Workshop so often get it wrong. When dealing with very complex rulesets (most GW games) a couple of games to "playtest" is simply not enough. You need to follow rulesets through and find the possible extremes.
Nothing says irony like spelling ideot wrong.
Nonsense. Excel complains if you go over 2^24 (approximately 17 million) cells in use (at least Excel 2007 does; I'm not sure about newer versions), but 1 million or so cells is easy. Make the formulas for one line, then copy and paste to a hundred lines. Or a thousand. Or ten thousand. Or, if you needed few enough cells per line, 1048576 lines by using Ctrl+arrow key.
And if that's not enough, change one unused value to reroll all of the random number generators and get a new trial with however much data you had before.
I'm not sure if you are just disagreeing with me for the sake of it now?
I did say that spreadsheets help (particularly with the use of colour) but what you appear to be describing is not a matrix like I drew - but a method of doing a Monte Carlo exactly as Overkillengine did.
I'm fine with Monte Carlos in the right applications (I used to be a Blackjack player and studied the game extensively - many BJ analysis are based on Monte Carlo runs) but it's not always appropriate in my view.
It's sometimes really handy to be able to compare odds as fractions for example.
Nothing says irony like spelling ideot wrong.