What are the odds for this ?

I have a question for you mathwizards.

I played at an onlinesite and lost for 15 straight hours. EVERY single hour my bankroll was smaller than the previous one. The 16:th hour I made a profit of 1 big bet then went on a 4h losing streak again (bankroll smaller than the previous hour). I then cashed out and never went back. I continued to play at the sites I usually play though. This happened at a new site for me. I didn't play for 20h straight. It happened during 4 days and the beats were just amazing.

My winrate at all limits I have played online so far is over 1 big bet an hour (over 2000h online) and my SD is about 10 big bets/h (actually smaller the higher the limit). I log all my sessions in StatKing.

For a losing player the odds of this event would of course be smaller but for a winning (like me) I guess it's pretty high. Just to flip a coin and get it tails 15 times in a row is pretty hard. Calculating that is not very hard.

But would anyone of you care to do the math including my winrate and SD in the calculations. I would be happy enough to get the odds for the first 15h and If anyone would do the math for all 20h even happier.

Sorry if my english is bad. Im from Sweden.

[Bozeman]

The probability that a 1BB/hr winner with a SD of 10 BB (1 hour) will proceed to lose the next 15 hours is ~9/1 million. Not exactly unheard of, but quite unlikely. My guess is that you were not playing better than your opponents here. However, note that the chance of a 1BB/hr player winning the next 15 hours is small as well (~ 10 times larger).

Craig

[BruceZ]

Heh, in this case we do want the odds of doing something so many times in a row, unlike the question on the other page.

If you are a 1 bb/hr player with sd = 10 bb/hr, then losing for an hour means being down 0.1 standard deviations which is 46% (assuming hourly results are normal). Losing 15 consecutive hours is (.46)^15 = 1 in 114,454. Only winning 1 in 20 is 20*(.54)(.46)^19 = 1 in 236,689.

Thanks for the replies.

I guess most recreational (winning) players will never encounter a streak like this during their lifetime, maybe not even professional players logging 2000h/year. After your replies I now know this is a streak that could actually happen but I think I'll stay out of that site for time being anyway. Don't feel comfortable with the never ending beats I got there. There's lots of sites out there where these things have never happened to me and I'll stick to them.

Thanks again for your calculations.