It is indeed a very beautiful question, and it's answer is also no short one. I will try to answer your question, by dividing your question to several parts.
1. Does believing in something because it's the safest bet really win you a ticket to heaven?
A: It depends, where your believe came from. Most of the times with us Humans, our belief and the safest bet is deeply connected to the religion, we are born in. A Believe must come after a research through different religions.
This research causes, respect towards other religions and provide a good comparison of Beliefs. So, If this belief comes after a good research, then the answer to your question is YES.
2. Doesn't God want you to be less self interested when it comes to believing in Him?
A: No, With the more belief in God, almost all the religion's pious people deviate from self interest to people interest, and it is the correct thing to follow, since following the self interest leads society no-where to, and helping the needy in the society is connected to less self interest.
3. Is brainwashing yourself into conviction a legitimate path to Islam or any Religion? (Most Important)
A: No, Brainwashing yourself into conviction is not a legitimate path to Islam.
The Definition of Brainwash "You essentially brainwash yourself into true belief, so that what starts out as self-interest can actually grow into an honest conviction." is legit.
This self brainwash may come as a result of not finding answers to your questions about your religion. The sensitivity of your questions deprive you to ask them, and it eventually leads to a self brainwash. This phenomena could also be result of many contradicting answers to the questions about your religion, and the confusion it creates led a person to embrace this brainwash.
This brainwash is the most devastating to happen to anyone. The downsides are so many, that it will prolong the answer too much, but I will try to cover some.
- You don't care about other religions and the people. The only thing you care about is your own religion and people.
- You don't respect, anyone out of your religion.
- You are easy to deceive into a wrong perception, led by a person from your religion.
- You ignore intelligent and good people from other religions.
- You give or take life, without understanding any value of life. and go on.
I as Muslim, do not follow this religion, as a brainwashed person. So the first thing to notice in me is, all those downsides in brainwashed people do not include in me. I follow Islamic rules, because it provides every right to each person in the society.
Islam has described rights of everyone, so high that, It is said, That God (ALLAH) may forgive you for his rights(worship), but will not forgive for rights of the people.
Islam has defined :
- Rules for war
- Rules for women/children/old people in war
- Rules for animals in war
- Rules for trees in war
- Rules for the dead bodies of enemies in war
- Rules for prisoners of war
- Rules for the rights of Prisoners of war
- Rules for water distribution(with enemies) in war
And many more. These rules are set, must to be followed or the respected penalty will be awarded, The picture drawn about Islam nowadays is the exact opposite of the reality about Islam.
I tried to put answer short. I missed some points on purpose to make this answer more concrete. I hope this helps.