Around 3 years back, I had a stall setup at my school's fun fair. It was a simple gambling setup. You put your money on either of 3 things: i] Above 7, ii] Lucky 7 or iii] Below 7. And then, you roll the dice [2 of 'em]. If you put on either below 7 or above 7 and the dice sums up to below 7 or above [resp.].. you get twice your money. On 'Lucky 7', you get thrice your money. Here obviously it depends on how the player chooses his bet that determines the expected value. Let's assume our player is quite fair.. he picks up either of the 3 categories with equal likelihood. So, what is the expected value for each $1 he bets?