How to calculate probability of winning bowl pool? I currently have a spreadsheet that keeps track of players and their respective picks as to who they think will win each college bowl game. At the beginning, before any game is played, each player has equal probability of winning the whole thing. What I'm looking for is an expression that will give me their updated probability after each bowl game is played.

In the example below, what is the probably (in percentage) of Braden winning the whole thing, given his score (5 of 8), everyone else's scores, and games played vs total number of games?
I wouldn't try to do this analytically, since such an analysis would probably have to make assumptions about the games that don't hold water (e.g., that the result of each game is $50$-$50$).

Instead, I would approach it with a Monte Carlo simulation.  As best you can, estimate the probability of each game's result.  One possibility is to use the Vegas odds.  This will take some care, since the odds will include the vigorish (the house percentage), so this has to be scaled down.

For instance, if the odds are given as money lines: Say the bet on Team A is $+170$ and the bet on Team B is $-200$.  That means that a bet of $\$100$ on Team A wins $\$170$ if they win, while a bet of $\$200$ on Team B wins $\$100$ if they win.

Converted into odds, those bets are $17$ to $10$ and $10$ to $20$ against, respectively.  Converted, in turn, into probabilities, that's $10/27$ and $2/3$.  Obviously, those add up to more than $1$, and the excess of $1/27$ reflects the vigorish.  These can be corrected in different ways, but the easiest is to scale them down to $10/28$ and $18/28$.

Once you've done that for each of the $33$ remaining games, run a Monte Carlo on them, and tally each person's score for every run.  A million or so runs should be enough to figure out winning probabilities to three significant digits.
I think a coin flip approach could be used. What are the odds of any given player to guess the most coin flips (game winners) correctly? Variables would be 1) number of guesses they currently have correct, 2) number of guesses other players have correct, 3) number of differences in the remaining picks they have with every other player, then 4) If every possible permutation could be ran, what is the probability that this player to have more correct picks. 

Can anyone set up the equation? 

To edit... for THIS scenario, players do not care about odds of winning based on who are the favorites of any given game, but odds of winning if EITHER team can win (i.e., coin flip). The favorites of the game do not matter. Rather, what is the mathematical probability that any one player can possibly win over the opponents.  Can anyone set up THAT equation?