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What is the probability of me losing a 3/1 bet 10 times in a row I've tried working out myself but the equations needed go straight over my head

user431055
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  • No matter how sophisticated your betting system at roulette, you will still lose, in expectation, a thirty-seventh of the the total amount you place on the table (two thirty-eighths in the U.S.A.). – John Bentin Mar 31 '17 at 10:33
  • As you was betting on first 3rd you perhaps should clarify your question regarding what kind of bet you did. – skyking Mar 31 '17 at 13:08

1 Answers1

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The probability of loosing one time is $2/3$, then to loose $10$ times in a row is $(2/3)^{10}$ (since the games are supposed to be uncorrelated). If calculated this equals about $1.7\%$.

For the record there is no such bet in actual roulette. There are 37 or 38 numbers (including $0$ and possibly $00$). The $3/1$ bets (such as dozen or column bet) actually only have a $12/37$ or $12/38$ chance of winning and $25/37$ or $26/38$ risk of loosing (giving the house a slight advantage). Then the risk of loosing ten times becomes slightly higher $(25/37)^{10} \approx 2.0\%$ or $(26/38)^{10} \approx 2.2\%$.

skyking
  • 16,654
  • 0.01734152991 would this be correct then or have I made a mistake somewhere? – user431055 Mar 31 '17 at 08:23
  • It is correct. Multiply it by 100 to get the percentage. – Abelois Mar 31 '17 at 08:24
  • @user431055 Yes, I'm rounding to one decimal. A more closer approximation would be $1.734152991%$, but still that's an approximation too. – skyking Mar 31 '17 at 08:25
  • Thanks i was betting this morning and I was betting on first 3rd and it lost 10 times before it came in a was just curious as the chances of me losing 10 times in a row was – user431055 Mar 31 '17 at 08:28
  • @user431055 Then you should use calculation in the second paragraph that takes $0$ and $00$ into account giving a slightly higher probability. Often one gets the probability wrong by intuition why is why somebody will suspect the game to be rigged (when they're loosing). – skyking Mar 31 '17 at 08:36
  • Yeah I thought I would be a much smaller chance than 2% thanks for explaining and showing me how to use equation – user431055 Mar 31 '17 at 08:42
  • A bet involving 3:1 odds gives a probability of winning of 0.25. You are perhaps forgetting that Black/Red, Odd/Even are also bets in roulette, so that such a wager is possible. – daniel Mar 31 '17 at 08:59
  • See Hubley's answer regarding the notation issue...https://www.quora.com/Betting-If-someone-says-theyll-give-me-3-1-odds-on-the-occurrence-of-an-event-what-does-it-mean. You may be right but I have generally seen 3/1 as meaning 3:1. – daniel Mar 31 '17 at 10:36
  • Let us continue this discussion in chat. – skyking Mar 31 '17 at 12:58