Alignment doesn't really work that way.
Alignment in latter additions of D&D isn't really intended to be a harsh white/black, can/can't model of the universe. It's a means of fluffing out characters that occasionally interacts with the rules in awkward ways for nostalgic reasons.
With that said, here's some rules:
"Good" implies altruism, respect for life, and a concern for the dignity of sentient beings. Good characters make personal sacrifices to help others.
Someone who transfers wealth to others while maintaining a state of poverty for himself definitely meets the criteria for "good."
"Law" implies honor, trustworthiness, obedience to authority, and reliability.
Are your character's opponents aware that they are playing for uneven odds? If so, there is nothing against Lawfulness. If not, then this is a lot of lying, which Lawful characters tend not to do.
On the other hand, a Vow is very lawful.
"Chaos" implies freedom, adaptability, and flexibility.
Flexibility, including some mostly harmless lying seems right up Chaotic's alley.
On the other hand, a Vow is not very chaotic.
All told, this character appears to closely match the description for Neutral Good:
Neutral Good, "Benefactor"
A neutral good character does the best that a good person can do. He is devoted to helping others. He works with kings and magistrates but does not feel beholden to them.
Neutral good is the best alignment you can be because it means doing what is good without bias for or against order.
But other alignments (even diametrically opposing ones) could apply.
Why Assigning Alignment to Actions Doesn't Work Very Well
Most alignment debates present a course of action, and ask what alignment the action is. The problem is, that there are three very different means of judging actions:
By the objective state of the action.
By the outcome of the action.
By the intent of the person committing the action.
Suppose a player is asked to save a small kingdom, and does so.
Saving kingdoms is a good action (objective state of the action), and therefore the character is Good, right?
But then suppose that in a subsequent war against Evil, Good loses because they spend too much time protecting the small kingdom you saved and the world ends (outcome of the action). Committing an action that results in the world ending is Evil, right?
Finally, consider a character who goes around saving small kingdoms deliberately to create a drain on Good's resources in the upcoming war. Machiavellian schemes are Evil, right?
The same action, three different ways of looking at it, and two diametrically opposed alignment judgments. Judging whether an action is good or evil is a very hard problem, and the designers don't give us any guidance on which criteria apply.
In fact all they give us is this:
Alignment is a tool for developing your character’s identity. It is not a straitjacket for restricting your character. Each alignment represents a broad range of personality types or personal philosophies, so two characters of the same alignment can still be quite different from each other. In addition, few people are completely consistent.
By RAW, you're allowed to violate your own alignment. Alignment is just intended as a guide... A way for you to signal what aspects of your character you want to focus on, and to help other players get a better idea of who your character is when you're not doing full-on immersion roleplaying.
A character who willingly and willfully commits an evil act loses all benefits from all his exalted feats. She regains these benefits if she atones for her violations.
Remember what I said earlier about awkward rules interactions for nostalgic reasons? This is a good example of a bit of rules text that hearkens back to a time when alignment was a lot more literal.
Unfortunately, the game gives very few tools for implementing this standard. I can say that cheating in this way doesn't appear to be objectively evil. It doesn't use positive/negative energy, or the [evil] descriptor, or any extraplanar forces of that nature.
It isn't as bad as the few examples of evil behavior (such as selling someone a cursed item).
In the end, it's likely to be a DM's call. Talk to your DM, and figure out what criteria they want to apply in cases like this.