"Bet your bottom dollar" is an English expression that is usually said when someone is absolutely certain that something will occur. The expression first became popular in the 19th century in the United States, where the dollar is the basis of that country's currency. When someone says "bet your bottom dollar," it implies that the person would wager his last remaining money on the chances that the event in question will come to pass. This is usually not a literal promise, and, indeed, the expression is rarely used in conjunction with actual gambling.
In the English language, idioms are used as a way of conveying meaning with a short phrase that is often colorful and expressive. These phrases are rarely meant to be taken literally, even if their origins have some basis in concrete or historical events. The English phrase "bet your bottom dollar" has been used in various literature, popular songs, and even election campaigns since the 19th century as a way to convey a high degree of certainty.
When a person tells another person to "bet your bottom dollar," he is essentially telling him that there is no doubt of the certainty of some future event. According to the person who says the phrase, whatever follows will, without any doubt, take place. As an example, someone might say, "You can bet your bottom dollar that we're going to win tomorrow." That means that the person is sure that his team will score a victory the next day.
The phrase gets its meaning from the fact that the "bottom dollar" would be the last dollar that a person would theoretically have. Anyone willing to gamble his last dollar on anything must be very sure that he will be right with his prediction. After all, the consequences of losing a bet with his last dollar would be great; he would lose all of his money if he lost that bet.
As a result, the idiom gains its impact from how forcefully it proclaims the speaker's certainty. In most cases, the speaker actually doesn't want the listener to risk his money on some random occurrence. In fact, it's also very possible that a speaker might use this phrase as an exaggeration of the likelihood of the event to which he's referring actually taking place. Sometimes the most colorful persuasion can turn out to be bravado in the end.