Quote from: 837204563;416959Hey, I share your feelings, but in my experience people get (unjustifiably) exited by crits.  And once when we were playing with a three-consecutive-twenties-is-a-kill rule, and when that extremely improbable event happened people were talking about it for a while.  But really I was just trolling Kyle who was willfully missing the point of a silly mathematical puzzle.

We had a similar house rule. I found it extremely exciting when it did occur, and can remember most of the instances when it did (twice for me personally - once on a demigod robot at the campaign climax, and once using the Magic Sword spell on an ancient red dragon).

The problem with your math is you are looking at statistical average.  The reality is that the results of the second coin flip have no baring at all on the first.  There is always a 50% you'll bust out on each flip.   While there is a statistical possibility you'll flip 7+ head in a row and score your uber damage.  The odds are stacked against you.  While you calculated the odds of success the odds of failure are the same.  

The 100 damage in this case is by far the better choice.

Quote from: kryyst;416990The problem with your math is you are looking at statistical average.  The reality is that the results of the second coin flip have no baring at all on the first.  There is always a 50% you'll bust out on each flip.   While there is a statistical possibility you'll flip 7+ head in a row and score your uber damage.  The odds are stacked against you.  While you calculated the odds of success the odds of failure are the same.  

The 100 damage in this case is by far the better choice.

That is the stupidest thing I have ever read. I think the entire universe may have gotten more stupid just by me having read that.

No one is ignoring the chances of busting. The chances of busting are built into the chances of not busting. The chances of busting and not busting always add up to 100%.

The issue is exclusively how many attacks it takes you to defeat an enemy. With the coin flip option you have a very tiny chance of defeating any enemy every time you attack. With the 100 damage option there is a specific number of attacks that any enemy will take to drop. If the number of attacks that the straight damage option is going to take is very high (in excess of 100), then the chances of dropping an enemy in one spectacular uber hit before attacking that many times is more than 50% and the coin flipping option is "better".

The issue is not the math. The issue is not your chance of going bust. The issue is 100% the fact that the break even point where you are more likely to kill your enemy faster with the coin flipping option is a point that few game designers will inflict on their players because very large numbers of attacks being required to drop enemies is tedious.

-Frank

You are a fucking idiot.   Yet we are in agreement, 100pts is the better option unless an enemy has so many hit points that the only probably way of defeating them is to luck out.   So your point is what exactly - to yell at the wind?

Statistics lie.

Or, as has been stated several times, your odds of even doing 100 points of damage with the coin flip method are minute. Please start flipping a coin and post when you get seven heads in a row.

Quote from: kryyst;417030to yell at the wind?

Some people genuinely enjoy "yelling at the wind".

Just turn on the television to any cable 24 hour news channel, or daily talk shows on the radio.  :rolleyes:

Please don't post politics. "No politics" is one of the reasons I like this site.

The math isn't wrong.  Please click on the link I provided earlier for a full explanation by people with PhDs.  I doubt that they are wrong.

So you managed to get 7 heads in a row already? How many tries did it take?

1, probability is a bitch, ain't it.  But that is irrelevant to the mathematics, as you surely are aware.

Quote from: Kyle Aaron;416947I would go for 100 since if I sit there flipping a coin all night the other players will get pissed off, quit the campaign, and then it won't matter how awesome my character is, I won't be playing them any more.

That's the sort of thing missing from your analysis, what actually happens at the game table. If you're going to ignore what actually happens at the game table you may as well head over to the Forge.

You could replace the coin flips with a custom d8, labelled 1,1,1,1,2,2,3,4.
On a 4, reroll and multiply.


Every copy of the St Petersberg RPG boxed set could come with a few of these...

Quote from: danbuter;417061Please don't post politics. "No politics" is one of the reasons I like this site.

...and a pre-painted Lenin miniature
(Sorry, couldn't resist)

The math is right, you 'expect' to deal more damage with the flipping method.

Unfortunately, you're only likely to be 'near' infinity (or at least really really high) after you've made an infinite number of attacks (or at least a really really large number of attacks, for the picky). When you consider that most of the damage will be 'wasted' (much like using a daily power on a minion on 4e), there's no real benefit to the flipping method.

There's a question of utility that needs to also be considered. This is why a lottery ticket, even though a losing proposition, really isn't that bad (at least for a single purchase). What you're doing to your finances at the loss of a single dollar is insignificant to what an extra 50,000,000 dollars could do for you. Putting a year's pay into tickets on the other hand...

You'd be advised to study a mathematical concept called a "martingale" if you want to begin learning about these things.

Quote from: Doom;417145Unfortunately, you're only likely to be 'near' infinity (or at least really really high) after you've made an infinite number of attacks (or at least a really really large number of attacks, for the picky).

This is literally the classic gambler's fallacy A high result is not more likely after a large amount of attacks than it is on the first attack.  You are, of course, more likely to see a high result in a large sample set than in a small sample set, but this is irrelevant to the expected value.  And so how many times you use the ability is irrelevant to the value of the "St. Petersburg power".  (Buying more lottery tickets means you are more likely to get a winner, but since buying another ticket doesn't affect the expected results of the other tickets it doesn't raise the value of buying tickets.  Similarly, one use of the power doesn't affect any of the others, so how many times you get to use it doesn't change its expected value.)  

Quote from: Doom;417145There's a question of utility that needs to also be considered. This is why a lottery ticket, even though a losing proposition, really isn't that bad (at least for a single purchase). What you're doing to your finances at the loss of a single dollar is insignificant to what an extra 50,000,000 dollars could do for you. Putting a year's pay into tickets on the other hand...

Of course if you reason like this you are open to a sorites paradox ...

Quote from: Doom;417145You'd be advised to study a mathematical concept called a "martingale" if you want to begin learning about these things.

The St. Petersburg paradox involves a single gamble, the martingale with an infinite series of bets.  The St. Petersburg paradox is paradoxical because a rational gambler should (in some sense) be willing to pay any amount for a single shot at the game regardless of whether further gambles are allowed.

Also, if you flip the coin 100 times total for the night (not unreasonable given that many uses would have you flipping more than once) the odds of a 10 heads streak (1024 damage) are a little under 10%.  See: http://wizardofodds.com/askthewizard/images/streaks.pdf

Shouldn't this whole 'puzzler' be in the Design & Development section?

Seems to be an awful lot of math & mechanics and very little roleplaying to it all.

Just wondering.


- Ed C.