Math or probability question...Thanks for the help in advance

What would be the odds of a player winning 14 straight months? I would use a coin flip analogy as the odds are really unknown. I came up with about .005 which is 5 in 1,000 or 1 in 200 if I am correct. It seems that the odds of winning 14 in a row should be higher as 7 straight wins seems like it should less than 1% which is 1 in 100. Maybe my equation is wrong, which would end up with wrong results. For example, 50% after 1 win, 25% after 2 wins, 12.5% after 3 wins, 6.25% after 4, 3.13% after 5, roughly 1.6% after 6 straight wins, .8% after 7 straight wins.

What am I missing??

Thanks again as the last question I posted, someone answered correctly!!

Quote: bigpete88

What would be the odds of a player winning 14 straight months? !

Winning what for 14 months? You mean leaving the casino a winner every time you played for 14 months? Did you go 5 times or every day?

Quote: bigpete88

What am I missing??

Generally speaking, what you are missing is the content on https://wizardofodds.com/

The probability of winning 7 straight coin tosses is (0.5)^7 = 0.0078125
The probability of winning 14 straight coin tosses is (0.5)^14 = 0.000061 (approx.)

I was not saying it was me. This player states that he is up 14 straight months. He goes 2-3 times a week and loses some days. I just wanted some math to go with this "story" that he is up 14 months straight. I thought coin flip would be close enough unless someone had a better equation. I know all about variance and standard devaition but not great with the math and equations!!!

Algle,

Thanks for the info. I knew someone could help. Please break down the 0.000061 as in 1 in 300 or 1 in 3,000 or ??? I have not had math class for awhile.

Thanks again!!!

Quote: algle

The probability of winning 7 straight coin tosses is (0.5)^7 = 0.0078125
The probability of winning 14 straight coin tosses is (0.5)^14 = 0.000061 (approx.)

To get the "1 in" result just divide the fraction by 1.
(0.5)^7 = 0.0078125 --> 1/0.0078125 = 1 in 128
(0.5)^14 = 0.00006103515625 --> 1/0.00006103515625 = 16,384

But the above answers can also be misleading. But they do answer your question of 14 days.
The probability for 7 in a row (given above) is only when there are exactly 7 flips or n=7.
Same with 14 in a row where n=14.

As n increases the probabilities also increase.
The average wait time for 7 in a row is 1 in 254 flips (SD 248.38)
50.1449428% chance of a run of 7 or more in 178 flips

For a run of at least 14 the average wait time is 1 in 32,766 flips (SD 32,753)
50.000004% chance of a run of 14 or more in 22,715 flips

Quote: bigpete88

I was not saying it was me. This player states that he is up 14 straight months. He goes 2-3 times a week and loses some days. I just wanted some math to go with this "story" that he is up 14 months straight. I thought coin flip would be close enough unless someone had a better equation. I know all about variance and standard devaition but not great with the math and equations!!!

It certainly is possible, but without knowing what games, stakes or bankroll management system he is using, it would be misleading to assume it is a coin toss. He could be a skilled poker player, in which case putting together more than a year of winning months is not unheard of. If he manages his bankroll with discipline, pressing only when he is ahead, and slowing or stopping play when he is dropping back to even, it would not be too difficult to end each month up at least $1.

Quote: Ayecarumba

It certainly is possible, but without knowing what games, stakes or bankroll management system he is using, it would be misleading to assume it is a coin toss.

Ayecarumba makes an important point here. A coin toss might be a very bad analogy. To take an extreme example, a player with a $100K bankroll would have very little trouble playing in a casino and trying to win $2K a month for 14 straight months making $100 bets. His risk of ruin is very low.

Notice, I said "low", not zero. A large bankroll is not a license to print money. Even this guy with the big bankroll, if he keeps trying to win $2K a month for five or ten years, stands a good chance wiping out his bankroll on a losing streak, unless he is an advantage player.

Guido,

Thanks for the math lesson. You are much better in math than I. It appears that the answer to my question is 1 in about 16,300.

Also, thanks for the added info on probability on how often this event happens.

This players "story" is that he has played about 250 short playing sessions over 14 months and is ahead every month. The best equation I could think of was to use a coing flip without having more data. Do you have any other input, comments, or overview on 100+ months looking forward given the data that I gave? There will be a lot of attention given to your next answer.

I liked your answer and the extra work that you put into the answer. Thank you!!!

Please take as much time to answer as I am looking at your info with the utmost respect. Please give much overview as you can. No rush.

Big P

Thank you so much for this response. Friends of mine that have a Hedge Fund agree with your comment that money mgt. is of utmost importance.

Do you think it is an advantage to press only when ahead and pull back when losing?

Any other input or comments that might help someone that might play semi-pro??

Thank You

Thank you for taking the time for the response. I am in complete agreement with your comments.

Thank you.

Quote: pacomartin

Even this guy with the big bankroll, if he keeps trying to win $2K a month for five or ten years, stands a good chance wiping out his bankroll on a losing streak, unless he is an advantage player.

Actually an AP is in just as much danger of wiping out his bankroll as a normal gambler - if the gambler can at least quit when he wants, as an AP you have to push it. There's nothing quite as frustrating as having your max bet out in a deck full of tens and aces you've been waiting so long for and seeing them all go, one by one, to the dealer, with your bet attached.