What might seem intuitive is to have a mixed strategy of 75% heads and 25% tails. Maybe something like 'flip an unbiased coin twice and bet tails if you get tails twice and heads for any other outcome'. What result will that give you?
There are four possibilities here:
- Coin lands on heads and you bet heads (75%*75% = 56.25% of the time)
- Coin lands on heads and you bet tails (75%*25% = 18.75% of the time)
- Coin lands on tails and you bet heads (25%*75% = 18.75% of the time)
- Coin lands on tails and you bet tails (25%*25% = 6.25% of the time)
1 and 4 are winning situations, so you'll win 62.5% of the time this way (just sum the 1 and 4 win rates).
You might immediately notice that 62.5% is less than 75%. What if you just always bet heads? Filling out the same list as above:
- Coin lands on heads and you bet heads (75%*100% = 75% of the time)
- Coin lands on heads and you bet tails (75%*0% = 0% of the time)
- Coin lands on tails and you bet heads (25%*100% = 25% of the time)
- Coin lands on tails and you bet tails (25%*0% = 0% of the time)
1 and 4 are winning situations, so you'll win 75% of the time this way. In this situation, the general win rate is:
(coin bias*head bet percentage) + [(1 - coin bias)*(1 - head bet percentage)] = win rate
(coin bias*head bet percentage) + [(1 - coin bias)*(1 - head bet percentage)] = win rate
We want to maximize this. Using b for 'coin bias' and h for 'heat bet percentage':
b*h + (1 - b)*(1 - h) = win rate
b*h + 1 - h - b + b*h = win rate
2*b*h + 1 - h - b = win rate
h*(2*b - 1) + 1 - b = win rate
At this point, we have an equation for a line. Win rate vs h is a line with a slope of 2*b - 1 and an x-intercept of 1 - b. Anytime 2*b - 1 is positive, this line will go up and to the right so h = 1 is the best bet (heads 100% of the time). Anytime 2*b - 1 is negative, h = 0 is the best bet (tails 100% of the time). 2*b - 1 is positive whenever b is greater than 0.5. Thus, the optimal strategy here is bet in the direction of the bias 100% of the time when you have a known, biased coin.
⚡️✳️CASINO Online💵 💲คาสิโนสด ชั้นนำระดับโลก
ReplyDelete♠️ บาคาร่า 🐡ยิงปลา 🦀น้ำเต้า
🎲ไฮโล ⚽️ บอล 🏟️ กีฬา 🎱 คาสิโน
👍เว็บตรงไม่ผ่านเอเจ้นท์ ฝาก•ถอน ระบบ𝗔𝗨𝗧𝗢💸
➡️ฝากขั้นต่ำ 1 บาท
➡️ถอนไม่จำกัดครั้ง 💯
➡️มีแอดมินดูแล24ชั่วโมง
➡️ไม่ต้องโยกเงินให้เสียเวลา💸
➡️รับทุกธนาคาร 🏧
It's tax-exempt - When you purchase or sell shares, get compensated profits or get revenue from a bank you should pay charges like stamp obligationlogin sbobet
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteTheir poker instruction currently takes on another measurement requiring further developed technique and concentration.poker qq terpercaya
ReplyDeleteFirst and foremost, Sports Betting Champ, John Morrison, is an incredibly famous sports handicapper, and expert card shark. In his 28 years, in the betting scene, he is yet to have a losing season. judi online24jam terpercaya 2024
ReplyDeleteIt is sheer imprudence to put down a tennis bet (or a bet on anything) with a "customary" bookmaker. บาคาร่าออนไลน์
ReplyDeleteMost speculators neglect to comprehend that the best strategy for accomplishing a sound and supported long haul benefit from hustling is to saved an amount of cash away from your principle funds, exclusively for the betting of ponies. 888vipbet
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteYou can easily and safely do this at various online sport betting sites.spbo
ReplyDeleteI am always searching online for storys that can accommodate me. There is obviously a multiple to understand about this. I feel you made few salubrious points in Attributes moreover. Detain busy, awesome career! 먹튀폴리스
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteThe Lightning Network enables faster and cheaper Bitcoin transactions by conducting them off the main blockchain.
ReplyDeletehttps://www.linkedin.com/pulse/relai-empfehlungscode-2023-05-bei-jedem-kauf-sparen-be-freela-qgq8f/