Jelly bean counting contest, or more precisely, guessing contest, can be seen at lot of places. My school's library start it annually. My third try is coming soon and I have gathered loads of experience, in fact, the 2nd one I joined, I was off only by 2 jelly beans, and the winner is also off by 2, but his number is lesser so he wins.

My goal is NOT to actually win the jelly beans, but HAVE the jelly beans.
What's the difference? Aren't the only way to get them is to win?
Not really... you will see it later.. my post name is misleading.. xD

There will be 3 level of seriousness in jelly bean counting contest, and I will explain each one of them in depth.

Level 1. idk, just lucky.
Nothing much to say about this level. Guess.

Level 2. I like to work 20 minutes on this...I didn't go to high school for nothing.
Let's assume you can only see the jar and the jar's content but can't touch it.
In this level, you want to approximate the number of jelly beans. Usual strategies:

1. Savvy~
If the jelly bean is in its original package, go to the super market and find one from the exact same brand, check out the net weight. and buy another jar of jelly bean from the same brand (smaller jar...), and weight individual jelly bean then find the average. divide the net weight by the average, you get approximately the same amount. Or you can get to the brand's website and it might just tell you how many jelly beans in that jar. Find out the previous year's winner's number, most of the times, people choses to use the same jelly bean brand.

2. Mathematica!
say, if the jelly beans are in a jar without any indication of it's brand. then you might have to use the volume method. This requires you to find the volume of the jar and the volume of individual jelly bean. To do that without measuring the jar directly(because you can't touches the jar, duh), try use trigonometry. Set up triangles by cast light from one point to the jar and then shadows on the wall, which then will be used to calculate the dimension of the jar by using similar triangles. same way to get the size of a jelly bean and then you are going to do the math. We know jelly beans can't tightly packed because it's not cubic shaped what should you do now? because we got the dimension, we can create a computer simulation program that randomly putting jelly beans into the jar and see how many come out each time1. I suggest the use of Mathematica. , take the number the arithmetic and geometric mean converges to. Basically, that will get a pretty good idea of how many jelly beans there are in the jar.

3. Classical Physics FTW^^
Ok, this is only useful if you can physically touch the jar...
Find out the force is acting on the jar. Think about the gravity, electromagnetic forces between atoms(here, both static friction and kinetic friction should be considered).
Now add a certain amount of force to the jar at a certain point for easy calculation. For example, project an simple shaped object with known mass and known velocity, find out the air friction coefficient to find the impact energy and then subtract the energy used for deformation. Or just push the jar with a weighing scale, find the distance the jar slide, and use the result found earlier, the kinetic friction(if no slide occurred, use static friction and find the lower bound of the jar's mass), calculate for the mass of the jar.
Now, to find out thee individual jelly bean's mass, you hav to consider momentum, record the movement of a jelly bean contrast with the movement of the jar and... figure the rest out.
It's also possible to use other methods, like using ideas from fluid dynamics, as long as it's possible to find out the mass of the jar.

Level 3. I'm deadly serious: power of sociality
It's Web 2.0 age now... the world is about social...

1. The power of other Level 1 contestants
I mean, even with everything I just told you, it's just not easy to get the exact number, and people might do the same thing and have better approximations. I wish you can have some more chances..
That's when people (usually, human) comes in
First, you have to do at least something in Level 2 so you can bribe the Level 1 contestants with "higher chance of winning but a bit lesser rewarding"2. show them the pyramid of risk and returns and convince them that it's worth it to stay in low risk. Then negotiate on how much jelly beans you will get if they win. After they agreed, you will become their representative and you assign them numbers. These playing cards allow a few tricks will be played out when you found out there is danger. The ones are not used to play tricks, spread them out in a small interval around the approximated number-- every 5 jelly bean one entry. And put your name down for the entry you think it's most likely to win.

2. Intelligence meets doom
Information is the most powerful weapon.
The most powerful act in the contest, is called the Sandwich of Actual Doom (SAD), relay on other player's count. Joe, choses 1500 to be his jelly bean count. It's extremely close to your approximation. Sacrifice 2 contestant, you can ensure Joe have a minimal chance to win, sandwich Joe's count by adding 1501 and 1499 in the pile. Muhahahahahahaa...
Now, some people who is also in level 3, will create false information to create wastes in your playing cards, be sure to check for reliable sources, and use lie detection methods.
At the same time, you have to create a cloud of lies... be sure to learn how to anti-lie detection.

3. Internet is a great place...
Web 2.0 everything... create a website about the jelly bean contest and get enough people to join it(and make sure your opponent can't find it out). Post all the information you gathered on that site, and use a digg like method to see how popular each count number it is... and use it as a reference to the number you will chose. Blog about this, many people might want to join the fight and post very intelligent comments, like "replace the jar of the jelly beans when no one is looking... go home.. count it up... and put it back...". Facebook it, add it to events, notes, groups...

Final Suggestion:
Don't over do it...

Bonus:
Few tips to anti-jelly bean approximation:
1. irregular jar shape
2. does not fill the jar
3. different mass for individual jelly beans
4. different volume for individual jelly beans
5. different density for individual jelly beans(kinda like the combine of the above 2)
6. hide something inside the jelly beans so people can't see
7. not allowing any information other than the view of the jar be accessed. (video camera record the jar in all perspectives and put the video up instead of the jar)

1. 1. Generalization: n-dimension hyper-jar can fit how many n-dimension hyper-jelly beans if the position of beans are random
2. 2. Don't say "lower risk but lower returns", because it doesn't sound great