Batch 3 - Class 256 - Probability in Gambling

• MartinShCol - 1.15 - In a line up of 10 soldiers, what is the least number of soldiers that can be picked in order of either ascending or descending heights? Assume that no two soldiers have the same height.
• Answer: Mark every person by two numbers - the max number of consecutive ascending chain he is part of, and max descending chain he is part of. No two people can have same (asc,des) pair (WHY?), hence with 10 people, someone must have a "4" in at least one of ascending or descending tag.

• Show kids a roulette wheel, and explain the odds (35:1, i.e. if you bet one and win, you get back 1 plus 35)
• Introduce concept of probability - equally likely events
• What is "random"? Is 0,1,0,1,0,1 sequence random? Why/ why not?
• What is more "random" 00000 or 01101? Why?
• If you get on a red square three times in a row, what are the chances of getting a red on the next one? (Independent events)
• Ask kids to figure out their chances of winning (5.26% house advantage)
• What if we place multiple bets? Expected value
• Prob-winning x Amount-if-win + Prob-Losing x Amount-if-lose
• Does the house advantage of 5.26% mean that a player will always lose? Why do players play then?
• No. "Volatility index". For example, in a toss of coins, what is the chance that a person wins with one toss? With two? 
• After a 100 games, the player still has a chance of leaving with +-$10 (for $1 per bet)
• Higher the volatility, higher can be the difference between expected and actual outcome
• Consider other types of bets - red versus black (1:1 odds). What are the chances of winning
• Strategies to beat - ask students what they could do
• Is there a winning strategy if you have unlimited money? (Martingale strategy)
• Casinos allow fixed limit tables, and will often spot such betting
• Practically, one will run out of money
• Predicting the quadrant where the ball will fall (Thorp and Shannon's wearable computer)
• Studying bias in wheel
• See real life Roulette exploits at https://en.wikipedia.org/?title=Roulette

• In a diwali mela, I have a game stall. I draw two cards from a deck of cards. You draw a third card and if that third card lies between my two cards, you win. Assume that all cards are ordered, so that no two cards have the same value (i.e. we have a tiebreaker mechanism, like the suit color). What odds would you be willing to take to play a fair game?