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99% confidence means you are accepting a 1% error on the ideal.
95% means that you are accepting a 5% error on the ideal.
It would be hard to get within 1% or 5% of the ideal with very few tosses. If you do a few tosses you may actually conclude that the coin is biased even if it's not. I suspect that within 10 or 20 tosses you should seriously approach your ideal 50-50.
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