Can someone please explain to me, in a common sense way, WHY i should accept if i've got a 72% of losing the game? Seems like if the odds aren't in your favor the best thing to do is NOT to hand the opponent 2 points.

Imagine you're a 49-51 underdog and the opponent doubles. Are you going to take (as an underdog!) or give up a point?

We would prefer if the cube stayed at 1 any time we're behind, but if we're only behind by a little, we win enough times with the cube on 2 to make taking less bad than dropping. It turns out that for money games the magic number of how often we need to win to make taking the cube worth it is around 25% winning chances.

Ok, here's the math.

Suppose you get to a position where you're 28% to win and 72% to lose. You agree to play this position 100 times.

If you drop all 100 games with the cube at 1, you lose 100 points.

If you take all 100 games, the cube is at 2 on your side. You lose 72 games for a loss of 144 points. You win 28 games for a gain of 56 points. Your net is +56 -144 = -88 points.

Which is better, losing 88 points by taking, or 100 points by dropping? You're losing in either case, but you're losing less by taking, so you take.

Robertie’s math correctly shows that losing 88 points is better than losing 100 points. Robertie intentionally simplified his explanation. He chose to not elaborate on the power of holding the cube. The fact is that sometimes when you win, your position will improve to the point where you have sufficient advantage to cube to 4. So many times, you will not just win two points but will win four points. Thus, you will do better than winning 28 games for 56 points. For instance, if your position improves 25% of the time to justify a cube to four points, you will win 72 points (21 wins * 2 + 7 wins * 4). Also, if you gammon your opponent, you will win 8 points. Good backgammon players sometimes love when their opponents double them. The power of the recube is tremendous.

Stanley

If you are more familiar with poker, think of a double as analogous to an opponent betting. You have a choice to either call or fold. Are there situations where you are less likely to win than lose, but a call is nonetheless correct? Certainly there are. If you have a flush draw with the proper pot odds, you certainly are correct to call. (I’m ignoring the option to raise to simplify things).

Well the situation when facing a cube is exactly the same. You already have one unit “in the pot” as does your opponent. An initial double is a “bet” of 1 unit. You can “fold” to that bet, ie pass the cube, or you can call the bet,ie take. The “pot” size is 3 units, the one “bet” by your opponent and the two already in the “pot”. You are therefore getting 3:1 “pot odds”, and the math is exactly the same as the analogous poker situation. You need to win 25% to break even.

As stizznan correctly points out, this is simplified, and much like poker, you often can “call” with less winning chance than that. Unlike poker, though, you sometimes need more winning chances. This is because there’s nothing in poker analogous to losing a gammon, doubling your loss. Often in gammonish positions your take point will be significantly higher than 25%.