Part I
Panasonic Cordless Phone$49
Paper shredder
$69
Grim Reaper Computer Speakers
$29
Laundry Sorter
$57
Hot Glue Gun
$44
Mini Snow Cone Maker
$39
Hooded Dog Vest
$19
Remote Control Candle Set
$29
Twilight Turtle Nightlight
$29
Scrabble Dictionary
$60
Realistic Owl Decoy
$32
Stainless Steel Steak Knives
$72
DIY Library Kit
$14
LED Shower Light
$49
Coffee Grinder
$24
Lava Lamp
$39
Personal Soundtrack Shirt
$39
Indoor Bark Deterrent
$49
Toddler's Sand Table
$54
High School Game Football
$43
Portable Tire Inflater
$89
Flexible Bowls
$17
Pool Ladder
$42
25-inch Beanbag Chair
$49
Telephone
$40
Folding Bookcase
$79
All-Weather Pet Bed
$24
Bluetooth Retro Handset
$29
MLB Glass Cutting Board
$25
Bug Vacuum
$59
Spice Rack Carousel
$41
Laptop Speakers
$11
Fly Fishing Kit
$33
Karaoke System
$74
Cuisinart Pizelle Press
$40
Utensils
$20
Tabletop CD/DVD Case
$29
Personal Soundtrack Shirt
$39
Chrome Laundry Sorter
$76
Guitar Chord Assist
$42
Pac-Man Potholder
$15
Sudoku Game
$30
Fitness Ball
$19
Aviation Instrument Coasters
$15
Potty Chair
$46
Classical Guitar
$66
Price is Right Plug-And-Play
$19
Hot Dog Roller
$59
Snow Goggles
$22
Cuisinart Pizelle Press
$40
Hand Crank Lantern
$19
Portable Stereo System
$57
Folding Bookcase
$79
Cordless Water Kettle
$31
Pasta Express
$12
Wake-Up Clock
$70
Wine Rack
$40
Fold-Away Clothing Rack
$22
Magic Bullet Express
$55
Zojirushi Coffee Marker
$98
Water-Filled Barbells
$49
Slow Cooker
$60
Tool Kit
$25
Light-Up Pool Fountain
$50
Crochet Hook Set
$44
Sandwich and Waffle Marker
$39
Framed Glass Mirror
$62
Radio Lantern
$40
Lap Desk
$37
Digital Bathroom Scale
$64
Dispenser
$33
Handy fan/cooler
$49
Ice Cream Maker
$54
Ladies Sport Watch
$16
Deshedding Tool for Cats
$34
Talking Thermometer
$69
Neti Pot Kit
$12
Computer and Book Light
$17
LED Bug Trap
$30
Part II
The Plinko Board is played for a cash prize of up to $50,000 and also awards small prizes(in this case medals). "Since the Plinko board is basically a giant binomial distribution machine, it would make very little difference in the end result to have you guys drag the chip anywhere you want."The probability for getting 10,000 and for getting 0 in the Plinko Board is highest when taking the middle position. Therefore is rational to take the middle position for gaining medals. Note that the probability of getting 5 times 10000 is 0.00153, that is about 1 to 651! Get ready for a long and boring medal!
Explanation
The reason is easy because every state is reachable by binary decisions. The chip can drop left or right with the same probability. But moving there are more possibilities to move straight downward than to move left or right. For example, after two steps, we have a chance of 1/4 to move left-left, 1/4 to move left/right, 1/4 to move right/left and 1/4 to move right/left. Since left/right and right/left result in the same state, we have three states with the probabilities 1/4, 2/4 and 1/4.The state's are distributed in a Pascal's triangle. The Prize of the Plinko Board is located in the 0th row. So if the player takes the middle coin, the probabilities are:
2/256 -> 100
16/256 -> 500
56/256 -> 1000
112/256 -> 0
70/256 -> 10000
So to sum up, the odds of getting the 3 top medals if you drop every chip from the middle are roughly:
$50,000 - 1/654
$41,000 - 1/82
$30,100 - 1/10
So if you play 10 times a day, you should have the $41,000 medal within a couple weeks, and the $50,000 medal within a couple months.
By shifting the chip to the left or right, both "extreme" prizes 0 and 10000 move closer to the edges of the Pascal's triangle, the probability of earning the medals decreases. Note that the probability of reaching "uninteresting" results like 100 or 500 would gain an additional probability due to reflection at the boarder!
Credits
Probability Explanation by Deomas and DiMonoGuide by duckyness
Ported to Wiki by EJR