Strategy for 7 up 7 down game This is a dice game where the host throws the dice and the players bet on 3 numbers - numbers below 7, 7 and numbers above 7. On numbers below and above 7 the players get double their stake and on 7 the players get 5 times their stake. For example if i bet 100 bucks on "below" and 7 comes, I will lose, but if 6 comes, then i win 200 bucks. Similarly if someone has betted 100 bucks on 7 and if 7 comes, he wins 500 bucks. 

What is the best way to bet in this game?
As they say, "the only winning move is not to play." I assume there are two dice. In that case, the expected value of all three bets is the same, and it's negative: on average, you lose $\frac{1}{6}$ of what you bet. 

Some details: when rolling $2$ dice the probabilities of getting a sum of $2, 3, 4, ... 12$ are $\frac{1}{36}, \frac{2}{36}, \frac{3}{36}$, and so on, increasing until $7$ and then decreasing. This is a nice exercise if you've never done it; you just need to count the number of ways a pair of numbers between $1$ and $6$ can add up to a given number. It follows that the probability of getting a sum of $7$ is $\frac{1}{6}$, and by symmetry the probability of getting above $7$ or below $7$ are each $\frac{5}{12}$.

It follows that if you bet $7$ then on average you multiply your stake by $\frac{5}{6}$, whereas if you bet either below or above then on average you also multiply your stake by $\frac{5}{6}$. So all three options are equally bad, in the long run.

Some meta-lessons to learn from this computation:


Generally the expected value of a game like this is negative, or the host would never bother to offer it. For example, the expected value of every game at a casino and the lottery has to be negative, or else the casino (resp. the institution running the lottery) would not make money. This is as much a lesson about incentives as it is about probability.
If one of the options was better than the others, at some point people would be aware of this and play only that option.
Dont worry about all these mathematics, make it simple, gambling is all about sheer luck. Doubling the loss bets isn't a good idea, I have lost many times doing that, even after 15 deals the side won't change, this can happen anytime, this is very risky attempt for someone playing with limited amount, and this idea will be successful for the one who have the money backed for the betting. Who knows how the cards are shuffled, then there is no point of permutations, combinations and probabilities. Please dont misguide people with this kind if advices. For me gambling is sheer luck to add some more money to our hard earned money  what I say is accept both loss and profit. And do not gamble with commitments, if u do that chances of losing is more than 100%