So let's try some math! The expected value of a given non-death roll (since in east Asian cultures 4 is associated with death I presume) is (1+2+3+5+6) / 5 = 3.4. Thus, each successful game requires on average 100 / 3.4 = 29.4 rolls.
The chances of rolling 29 non-4 die rolls in a row can be calculated like this: not rolling a 4 is a 5/6 chance, and since we have to do that 29 times we have to multiply by itself 29 times, so (5/6)^29 is .00506, which is a .51% chance of success. Taking the inverse by raising it to the -1, we see there's a 1 in 198 chance of rolling 29 non-4s in a row. (Or more accurately if we use 29.4 we get 213)
But I got a B- on a probability test once, so let's check that math with a program:
function bestGame()
{
var sum = 0;
while(sum < 100)
{
var roll = parseInt(Math.random()*6) + 1;
if(roll == 4)
{
return false;
}
sum += roll;
}
return true;
}
function testGame(trials)
{
var wins = 0;
for(var i=0; i<trials; i++)
{
wins += bestGame();
}
return wins / trials;
}
testGame(100000);
And when run, I got a value of .00483 (though it varies a little each time), or a 1 in 207 chance of winning, and that's pretty close to our ideal value.
Thus, it looks like your chance of winning is actually about 1 in 213, because that's the ideal value.