[Sandwich]

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Yes, thanks... sorry I misunderstood you.
I appreciate it.
So, when I sit down to play this hypothetical game until a Big Win or a 6 flip in a row Loss (whichever comes first), I can expect to have a Big Win 85% of the time. And therefore I can expect to have a 6 flip in a row Loss 15% of the time.


(this is with a 50-50 coin... does this change much with a 48-52 coin or a 44-56 coin?)

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Right. The odds are about 85-15 in your favor for a Big Win vs a "Streak Loss" of 6 in a row.

Suppose the coin gives you only 48% chance of a good flip. This would equate to playing a Casino game paying even money with a 4% edge to the Casino.

You have .52 chance of 1 bad flip, so .52^6 = 1.98% chance of 6 bad flips in a row. That's about a 98% chance for the one time little win of Avoiding a Streak Loss of 6 in a row. Taking the .98^10 you get about 81.9% chance of a Big Win of 10 little wins in a row.

For a 44% coin, .56^6 = 3.08%. A little win is about 96.9%. A Big Win is 73%.

So if you're using this to play a minimartingale betting system you'll find yourself running into Streak Losses of 6 in a row with uncomfortable frequency.

PairTheBoard

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"uncomfortable" is relative.... [img]/images/graemlins/wink.gif[/img]

An 82% chance of winning $100 and an 18% chance of losing $630... yes, it's a gamble... but it might be fun to try, once.... I've never put $160 (let alone $320) on the blackjack betting circle before.....

Thanks again for the explanation.