I'm in a contest where I have to pick the outcome of 5 sporting events per day. Recently they introduced a feature where you could win money based on achieving streaks of days where you get at least 3 of the 5 picks correct. In the 5 months I've played the game my picks have averaged 63% (I'm keen to calculate betting odds and individual games range from 50% to almost certainties; one recent pick was -1800). Using this I get 73.3% chance of getting at least 3 correct. The prize table goes as follows (and I've calculated the odds using the compounded 73.3%):
Using the above my best option is the 6 days for $6 method as it generates a $0.93 EV.
The newest update includes a feature where if you go 5-for-5 (roughly 9.92% chance using a 63% individual pick rate) it increases your streak by 2 days instead of one. I don't know how to incorporate this in the above math. I tried to calculate it as .6337 (odds of 3 or 4) +.0992*2=.8322, but I feel this no longer reflects the odds of getting less than 3.
Lastly, as the above is predicated on the assumption of a long-term 63% can anyone suggest how to use odds for an individual day once known. For instance if I know a certain days picks give me a 60% or 80% chance of streaking, should I keep going or stop.
Any help would be much appreciated! Also I don't know if it's against the rules of this forum but I can provide the name of the game and my referral code if anyone is interested.
| Days | Prize | Odds | EV |
| 2 | $ 1 | 53.73% | $ 0.54 |
| 4 | $ 3 | 28.87% | $ 0.87 |
| 6 | $ 6 | 15.51% | $ 0.93 |
| 8 | $ 10 | 8.33% | $ 0.83 |
| 10 | $ 20 | 4.48% | $ 0.90 |
| 15 | $ 50 | 0.95% | $ 0.47 |
| 20 | $ 250 | 0.20% | $ 0.50 |
| 30 | $ 1,000 | 0.01% | $ 0.09 |
| 50 | $ 100,000 | 0.00% | $ 0.02 |
| 60 | $ 1,000,000 | 0.00% | $ 0.01 |
The newest update includes a feature where if you go 5-for-5 (roughly 9.92% chance using a 63% individual pick rate) it increases your streak by 2 days instead of one. I don't know how to incorporate this in the above math. I tried to calculate it as .6337 (odds of 3 or 4) +.0992*2=.8322, but I feel this no longer reflects the odds of getting less than 3.
Lastly, as the above is predicated on the assumption of a long-term 63% can anyone suggest how to use odds for an individual day once known. For instance if I know a certain days picks give me a 60% or 80% chance of streaking, should I keep going or stop.
Any help would be much appreciated! Also I don't know if it's against the rules of this forum but I can provide the name of the game and my referral code if anyone is interested.
