I DID make an error in my posting - it is a binomial distribution and a Bernoulli variable, not a Bernoulli distribution.
Nevertheless, the stats is exactly correct.
I also wrote a small program to simulate what happens when a bettor makes 1,000 bets at a 1 percent disadvantage.
After one million rounds of 1,000 bets each, that is, one billion bets, the results are
Player profits 250,803 times 25.333636363636362 %
Player loses 718,707 times 72.59666666666666 %
Just about exactly as predicted.
I think you've made some sort of mistake somewhere. The number of times a gambler wins a 49.5% game is a binomially distributed random variable.
The mean number of wins in 1000 bets is n*p = 1000*0.495 = 495
The 95% confidence interval for the number of wins in 1000 bets is 464 to 526.
The probability of winning only 253 time in 1000 bets is 2.39608e-55.
If you need proof via simulation, here's a quick one for R:
mean(replicate(1e06, sum(rbinom(1e03, 1, 0.495))))
var(replicate(1e06, sum(rbinom(1e03, 1, 0.495))))
It's pretty slow though. Otherwise you could read up a bit on the binomial distribution.