The home nation, without a coach, are licking their wounds from a disastrous tour of South Africa. Sri Lanka have just had their worst year in international cricket. And Zimbabwe are on edge after a thrashing by the Proteas that blunted their run-up to a crucial World Cup qualifying tournament in March.
The event, staged at Dhaka's Sher-e-Bangla National Stadium, is Bangladesh's first home engagement in more than a year, and follows three heavy ODI defeats in South Africa in October.
The task has been made more difficult by the resignation of coach Chandika Hathurusingha, who chose to return to his native Sri Lanka. Hathurusingha makes his debut as Sri Lanka's coach in this tournament.
Former national captain Khaled Mahmud is in interim charge as team director, and the Bangladesh Cricket Board has yet to indicate when a permanent replacement will be named.
Hathurusingha travels to Bangladesh with his own problems, as his new team come out of a demoralising year.
Former World Cup winners Sri Lanka won only five of 29 one-day internationals in 2017.
The country's cricket authorities changed captain twice in six months after influential all-rounder Angelo Mathews stepped down in July, highlighting the turmoil in the national game.
Mathews has been re-appointed as Sri Lanka's limited over captain ahead of 2019 World Cup, for which they were the final team to qualify.
Meanwhile underdogs Zimbabwe, who face Bangladesh in the first game of the tri-nation competition Monday, are looking for a lift ahead of hosting a World Cup 2019 qualifying tournament in March.
Last month they lost a Test in South Africa by an innings and 120 runs inside two days of what was intended to be a historic four-day day-night Test. The match lasted just 907 balls.
Zimbabwe will be boosted by the return of Brendan Taylor and Kyle Jarvis, who have not played one-day internationals since 2015 and 2013 respectively.
Coach Heath Streak has indicated that Zimbabwe will devote more energy to one-day games, due to limited Test opportunities.
The three teams will play each other twice in the two-week tournament, which ends with a final on January 27.
Mashrafe Mortaza (capt), Shakib Al Hasan, Tamim Iqbal, Imrul Kayes, Anamul Haque, Mohammad Mahmudullah, Mushfiqur Rahim, Sabbir Rahman, Nasir Hossain, Mohammad Mithun, Mehedi Hasan, Mustafizur Rahman, Abul Hasan, Rubel Hossain, Mohammad Saifuddin, Sunzamul Islam
Angelo Mathews (capt), Upul Tharanga, Danushka Gunathilaka, Kusal Mendis, Dinesh Chandimal, Kusal Janith Perera, Thisara Perera, Asela Gunaratne, Niroshan Dickwella, Suranga Lakmal, Nuwan Pradeep, Dushmantha Chameera, Shehan Madushanka, Akila Dananjaya, Lakshan Sandakan and Wanidu Hasaranga
Graeme Cremer (capt), Hamilton Masakadza, Solomon Mire, Craig Ervine, Brendan Taylor, Sikandar Raza, Peter Moor, Malcolm Waller, Ryan Murray, Tendai Chisoro, Brandon Mavuta, Blessing Muzarabani, Christopher Mpofu, Tendai Chatara, Kyle Jarvis