contradiction to law of large numbers? please explain

[csuf_gambl0or]

ok so my (idiot)friend was trying to tell me about his super blackjack system that he thought of. It was basically a martingale system. I was trying to explain to him why its a stupid system and it doesn't work.

He kept saying that if you lose like 7 hands in a row, the chances of you losing the next hand go down and the chances of you winning go up. He compared it to the use of a coinflip.

I kept trying to tell him that each hand, or each coin flip is an independent event. The last hand/flip has no impact on the next one. If the last coinflip was heads, the next flip has the exact same chance of landing on heads as the last flip, they are independent events.

But here in lies the problem. The law of large numbers states that over time, the events should even out. This means that if a fair coin is 50/50 to land on heads or tails then if the coin is fliped say 40,000 times, it will approximately land 20,000 on heads and 20,000 on tails. So if a coin lands on heads 10 times in a row, then theoritically the chance of the next flip being heads GOES DOWN right?!?! But how can this be? Doesn't the theory of independent events and the law of large numbers contradict each other? Someone please explain and clarify for me.