Does anyone know the exact math on the turtle dropping? I was wondering if it works off successful catches or as an overall percentage. If this doesn't make sense, I've provided an example...
Lets say I have 1 fishing skill and I'm fishing in Northrend pools, so I should have about a 1% successful catch rate. Is the turtle a percentage of that one catch? 1% (Successful catch rate) of 0.1% (Turtle drop rate)? Or is it in fact just 0.1% of catches in that pool?
I doubt the turtle is actually 1:1000. The drop rate is probably actually lower than 0.1%. It might be 0.05% (1 in 2000) or as low as 0.02% (1 in 5000).
Each catch is independent of all the other catches.
It's like flipping a quarter. You know every flip you have a 50% chance of heads, and a 50% chance of tails. Just because the last 20 flips were heads doesn't mean anything, your next flip you still have a 50% chance of heads and a 50% chance of tails.
So with the turtle being as rare as it is, it is completely possible (although unlikely) to cast a hundred thousand times and never catch him.
Did that answer your question, or am I missing the mark? I had trouble understanding what you were actually asking.
Edit: I reread your question, and no, you cannot catch the turtle along with junk...so only non-junk catches have a chance of having a turtle mount.
Your second edit answered my question. I was wondering if it was more effective to fish at a skill of 1, thus enabling me to fish from the pool for a substantially longer time. But seeing as it only drops from non-junk catches its not worth it.
Also, its not exactly like flipping a quarter, every time you do not catch the turtle, your chance to catch it increases slightly. Its not exactly '50%' every time to use your coin argument, if you don't get a head X times in a row, the chance of getting it on your next flip is substantially higher then 50% as X approaches infinity.
Every successive cast has the same loot table as the previous casts, and your odds do not change. If you have a 1 in 5000 chance of catching the turtle mount on your first cast, provided all other conditions are the same, you have the same 1 in 5000 chance on your 5000th cast.
Going back to the coin argument, every individual flip is a 50% chance of heads and a 50% chance of tails, regardless of any previous coin flips.
Speaking in terms of future flips, however, you have a 50% chance of landing on heads once, a 25% chance of landing on heads twice, a 12.5% chance of landing on heads three times, a 6.25% chance for four times in a row, a 3.125% chance for five times in a row, a 1.6125% chance for six times in a row, and a 0.80625% chance for seven times in a row.
However, even if you get heads seven times in a row, your next individual flip is 50/50. Period.
If you have a 1 in 5000 chance of catching the turtle, and you have cast 1,000,000 times already, your next cast is a 1 in 5000 chance of catching the turtle.
Multiplicative odds only refer to future events if there is a base chance of something happening, as each chance is individual of all others, and past/future misses or failures are not considered on the loot table.
Gummo <The Pacifist>, 6 months ago:Here are some odds using various drop rates...
If you fish until you have 5000 successful Northrend pool catches, and the odds of the turtle are 1 in 2000, there's a 92% chance you will have caught it by then; if the turtle drop rate is 1 in 3000, the chance is 81%; 1 in 5000 gives 63%.
You are exactly right, and I believe that was what TogTogTogTog was eluding to...but it doesn't matter how many casts you do, your odds of not having fished up what you were trying to get lower and lower with more and more catches, but that doesn't change the fact that every successive cast has the same independant catch rate as previous casts. So you can use that as predictive analysis to see about how long you should be able to get it in...but you can't say with certainty that "if I don't get it in X number of casts, my next cast has to be the turtle based on statistics". It just doesn't work that way.
Every cast has the same horrible percentage rate of getting what you're trying to get as every previous cast under the same conditions,
Using different variables (time of day, type of pool, etc) may or may not change the odds, but that has nothing to do with statistical analysis.
Another way to look at this: If you have done 10k casts without luck you have gotten exactly as far as when you just started. The accumulative percentage purely states how lucky and unlucky you were compared to a large number average, but it doesn't describe at all when you will get it.
Basically there extremely rare drops are like rolling a 1/(1000 to 5000) dice over and over again until you get a 1. As the dice has no memory, each roll is the same as the first one.
Well put!
http://math.arizona.edu/~ercolani/pyzdek.pdf is a paper on WoW about their WoTLK introduction of "Progressive Probability" where the chance of getting your quest item to drop approaches 100%. Seems like this applies to quest items though - not random drops like the turtle. Agree with above math about the turtle. However, see below... ;D
Nassim Taleb:
"Brooklyn-born Fat Tony and academically inclined Dr John, two of Taleb's creations. You toss a coin 40 times and it comes up heads every time. What is the chance of it coming up heads the 41st time? Dr John gives the answer drummed into the heads of every statistic student: 50/50. Fat Tony shakes his head and says the chances are no more than 1%. 'You are either full of crap,' he says, 'or a pure sucker to buy that 50% business. The coin gotta be loaded.' The chances of a coin coming up heads 41 times are so small as to be effectively impossible in this universe. It is far, far more likely that somebody is cheating. Fat Tony wins. Dr John is the sucker. And the one thing that drives Taleb more than anything else is the determination not to be a sucker. Dr John is the economist or banker who thinks he can manage risk through mathematics. Fat Tony relies only on what happens in the real world."
Actually you are incorrect about the dice as you wouldn't have gotten just as far as when you started. While the accumulated percentage while yes, stating how lucky/unlucky you are, also directly impacts your future rolls. While the above posters are correct about it being a '50/50' chance each time, the overall chance is still increasing allowing you to with a certain number of rolls, predict with nigh on certainty what your next object fished will be.
Example. Assume the drop rate is 0.001 for the Sea Turtle.
After 500 loots, the chance of seeing at least one Sea Turtle is 39.3%.
After 1000 loots, the chance of seeing at least one Sea Turtle is 63.2%.
After 2000 loots, the chance of seeing at least one Sea Turtle is 86.5%.
After 4000 loots, the chance of seeing at least one Sea Turtle is 98.2%.
After 7500 loots, the chance of seeing at least one Sea Turtle is 99.9%
This number will never hit 100%, but it can hit 99.9r% which in most circles 99.9r is considered to equal 1%. But lets not get into that discussion :P
Yes, you can use predictive analysis to see how many casts you will need to do from this point to reduce the probability of not catching the rare catch to such a small extent that it's not feasible to not catch it. However, your numbers are a bit jaded.
Assume the drop rate is .0002 for the Sea Turtle. That sounds a bit more accurate. Now, in order to get your chance of seeing at least one Sea Turtle to that same 99.9% you mention, means you will need to perform over 50,000 casts, if my math is correct.
But even if you cast 50,000 casts and didn't see the turtle at all, your next cast is still a 1 in 5000 chance (assuming those are the odds...because 1 in 1000 is WAY too optimistic).
The system outlined in the paper you linked does affect quest items, but nothing else. Since there is no driving force in the game for the fishing loot tables, no NEED to give any one item a higher priority than any other (who knows, maybe you're just questing for the fish in that area....you don't have a quest that tells you to get the turtle), every cast will use the SAME loot table, and you won't have progressively better odds cast-for-cast in the manner in which you describe.
TogTogTogTog wrote:
Actually you are incorrect about the dice as you wouldn't have gotten just as far as when you started. While the accumulated percentage while yes, stating how lucky/unlucky you are, also directly impacts your future rolls. While the above posters are correct about it being a '50/50' chance each time, the overall chance is still increasing allowing you to with a certain number of rolls, predict with nigh on certainty what your next object fished will be.
Your interpretation is wrong. Your numbers are right. It's completely false to state that "also directly impacts your future rolls". It does in no way impact your future rolls. It only impacts how unlikely the sequence you actually got from all possible sequences is.
See accumulative probabiliy says less than people think.
Accumulative probability does not say that if 10 people do n casts and the accumulative probability being X that 10*X people will see the event. Accumulative probabilities are also subject to the law of large numbers. I.e. if your probe pool is small even if your accumulative probability says 90% should get it, testing with 10 people it is possible to see fewer than 9 people not seeing the event!
Dice or these nonprogressive random loot evens have no memory, so every cast is 1/5000. If you did 7500 loots without luck there is nothing that stored that your chance of getting it with the number of tries was 99.9%. So for the point of how likely it is for the next 7500 you have gained nothing. Past events have exactly no influence on future ones.
Let me describe this difference in another way. There are two numbers here. One describing your past bad luck and one describing your chance looking forward given that you plan to do N tries.
There is no uncertainty about the past. If you did N casts and didn't get the event with probability X, then your bad luck was 1-X. It's set, you simply did not get the event and that's it. There is no actual uncertainy involved.
For future expectations, you still have this uncertainty and an actual chance that X happens.
Now lets put the two together. You did N casts and got nothing. Your expectation looking forward to get event X is not that of 2*N attempts, because there is no probability attached to the past N events at all anymore. Your probability looking forward is again just X for the N attempts unattempted!
So paradoxically if you have done say 7500 casts and got nothing, the next 7500 cast have the same (and not more!) expectation to them as the first 7500 you did.
If this was not true, then the probability would not be constant for each event. But it is. Or in other words, probability would depend on time and/or have memory. This isn't the case.
But I wish you were right. My main critique of fishing achievements is exactly that there is no sense of progress. I have done over 11k casts for the turtle and got nothing. All I can say to that is that in the past I was insanely lucky and for the future I haven't gotten anywhere yet. For all I know I can be equally unlucky again and do another 11k without luck! Random loot is really random.
After 11k casts I do not have neigh 100% chance to get the turtle next cast. I still have a 1/5000 (or whatever the actual rate is) chance to get it. So basically what you state is just not correct. The longer I cast without a catch, the more unlucky I get. That is all. The local probability doesn't change at all. In a large pool of people some will have gotten theirs early making the statistical mean (over large number) work out to 1/5000 casts being a catch, they just not happen to be mine ;)
donquixote235 <Angler>, 6 months ago:I actually dug up the formula for statistical probability while I was trying to catch the Magical Crawdad. Here's the way it works:
1-(F^T)
F = the failure rate (in other words, the chance of NOT catching the turtle, which we'll assume is 1999 out of 2000 times, or a 99.95% chance of NOT catching him).
T = the number of tries.
So, over time, your chance to catch the turtle (assuming a 0.05% catch rate) is:
1 Cast: 0.05%
5 Casts: 0.25%
10 Casts: 0.5%
50 Casts: 2.47%
100 Casts: 4.88%
500 Casts: 22.13%
1,000 Casts: 39.36%
5,000 Casts: 91.8%
10,000 Casts: 99.33%
Note that these figures are assuming that you haven't thrown the first cast... in other words, they're estimates about what you MIGHT catch over 10,000 casts. However your chance to catch it on each individual cast remains at 0.05%.
In a nutshell: you may luck out and get it on your first cast, but you'll be extremely lucky to do so. In all probability you'll have to cast at least a couple thousand times into pools to get the turtle.
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