I need Statistics Info on Hi-Low odds in a 0 to 999 game of chance

Question

I am working on an algo for a hi-low game that has 0-999 and I would like to know what the odds are of getting a string of consecutive rolls of 499 and under. Apparently it is different than a 50/50 chance, I have had a string of maybe 13 or 14 consecutive "losses" and lost all the tokens I was playing with. I am trying to arrange a situation where the odds are astronomically AGAINST losing all the tokens. It allows the "stake" to be doubled with each loss, so I get back the losses rather quickly. So I need to know how many consecutive losses is "impossible" and build my starting token count accordingly. "IF THE GAME IS HONEST" it should be possible to never lose all the tokens before I win them all back. Statistically Speaking ;)

Answer 1

 

 The probability of it happening once is in fact 1/2

 

 But if the game is "HONEST" as you say, the probability of getting 0-499 consecutively gets cut in half

with each trial.

 

   So for 2 trials, the probability is 1/2*1/2 = 1/4

            3 trials,  the probability is 1/8

 

  In general, the probability is (1/2)^N where N is the number of trials

 

 Not looking good is it?