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Joined: Jun 21, 2012
May 13th, 2022 at 1:38:34 PM permalink
Hi Mr. Wizard,

I have a quck question on online 8-deck Bacarrat.

What are the probablity of the Player wins 7 in a row? Assuming I want to bet Banker to win on the 7th, 8th, or 9th hand?

I followed your calculation, and it's (0.49317571)^6 =0.0143883194. Is this correct?

If I want to win only on the 7th, 8th, and 9th hand, using martingale betting system, (1, 2, 4...), what is the probablity of winning using this strategy?

Does it matter if I observe the game and see that there is a big difference in the wins by Player over Bankers's win?
For example, if Player's wins is 10+ more than that of the Bankers?

Thank you! If anyone or Mr. Wizard can answer my quesitons?

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Joined: Jun 22, 2011
May 13th, 2022 at 1:56:21 PM permalink
It looks like you don't want to know what the probability is of the player winning 7 in a row, but the probability of the banker winning any of the next three hands after the player wins 6 in a row. For all intents and purposes, this is the same as the probability of the banker winning at least one of any three consecutive hands, regardless of who won the previous 6 (or previous 60, or 600, for that matter).

Let me put it this way: replace baccarat with tossing a coin.
The probability of seven consecutive heads is 1 / 128.
However, the probability of six consecutive heads followed by a tail is also 1 / 128.
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