How do opponents respond to the Grace Gambit?

If you reject Pascal's Gambit, then you should also reject Thomas' Gambit(tm) for the same reason: it is incomplete.

Premise 1) You desire Salvation.

Premise 2) There is a chance that belief in Grace provides Salvation.

Premise 3) If belief in Grace does not provide Salvation, then doing Good Works provide Salvation.

Conclusion: One can achieve Salvation by both believing in Grace and also doing Good Works.

The problem with this gambit is the same as the problem with Pascal's: its premises are unsupported*. Without being able to inspect those things that actually cause Salvation, and to be able to report back with results you're left with guesswork and tradition. You could easily add a fourth premise that both believing in Grace and doing Good Works does not provide Salvation and it would all make just as much sense. Indeed, some critics of Pascal's Wager do add this kind of premise to point out the hypocrisy of the situation.

So essentially you're just left with faith. (YMMV as to how much of a 'just' that is)

(*Aside: Similarly, there's no reason for Pascal to conclude that believing in the Christian god will not have a negative effect. For example, one could posit a deity that for all intents and purposes acts exactly the same as the Christian god -- Moses, Jesus, Bible and all -- except that those who would be sent to heaven or hell by the Christian god are instead sent to hell or heaven respectively by the posited god. Without being able to inspect those souls that are sent to heaven or hell and for what reason, there's no evidential basis on which to form a conclusion as to which god one is praying; just faith that it is the one you hope.)

Hah, when I first heard about this theory, I thought it made sense. but to God, it does not. You may have heard about the story of two sinners who were hanged left and right of Jesus, where one sinner did not repent, however the other one did, and became the first one to enter the paradise with Jesus. IMO, I think the creater of this Gambit heard about this. The thing is, yes, you could enter the heaven after first Resurrection if you believe that the Jesus is your savior and only way to God is through him. However, the interesting fact is, God judges on on how much time you had to accept Jesus as your savior. For the sinner who was hanged, he had little time, he was slowly dying, but he lucked out. :) However This is different for other people who had more time. If you had more time, and had ability to serve Christ in any ways, he or she should have served the Christ. Besides, this life is only passing. How we do on our short lives are the only way to have better life at heaven. Take one parable Jesus made for example:

Matthew 24: [14] “Again, it will be like a man going on a journey, who called his servants and entrusted his wealth to them. [15] To one he gave five bags of gold, to another two bags, and to another one bag, each according to his ability. Then he went on his journey. [16] The man who had received five bags of gold went at once and put his money to work and gained five bags more. [17] So also, the one with two bags of gold gained two more. [18] But the man who had received one bag went off, dug a hole in the ground and hid his master’s money. [19] “After a long time the master of those servants returned and settled accounts with them. [20] The man who had received five bags of gold brought the other five. ‘Master,’ he said, ‘you entrusted me with five bags of gold. See, I have gained five more.’ [21] “His master replied, ‘Well done, good and faithful servant! You have been faithful with a few things; I will put you in charge of many things. Come and share your master’s happiness!’ [22] “The man with two bags of gold also came. ‘Master,’ he said, ‘you entrusted me with two bags of gold; see, I have gained two more.’ [23] “His master replied, ‘Well done, good and faithful servant! You have been faithful with a few things; I will put you in charge of many things. Come and share your master’s happiness!’ [24] “Then the man who had received one bag of gold came. ‘Master,’ he said, ‘I knew that you are a hard man, harvesting where you have not sown and gathering where you have not scattered seed. 25 So I was afraid and went out and hid your gold in the ground. See, here is what belongs to you.’ [26] “His master replied, ‘You wicked, lazy servant! So you knew that I harvest where I have not sown and gather where I have not scattered seed? [27] Well then, you should have put my money on deposit with the bankers, so that when I returned I would have received it back with interest. [28] “‘So take the bag of gold from him and give it to the one who has ten bags. [29] For whoever has will be given more, and they will have an abundance. Whoever does not have, even what they have will be taken from them. 30 And throw that worthless servant outside, into the darkness, where there will be weeping and gnashing of teeth.’

In short, you have to the best you can with the time and talent you receive, to make the best of it towards The Christ, and essentially our everlasting life in heaven. If you are like this: "Ok, I believe and accept Jesus as my savoir, now I can do anything I want now".

His life in everlasting life in heaven are not guaranteed. God judges that, but believing in Jesus and doing nothing towards your life in heaven is real bad.

The act of believing in salvation by grace is itself a work.

I cannot accept the wager; grace must be accepted via a work, 'working together with faith', as St. James puts it.

Secondly, this makes a weird dichotomy that I'm not sure how to parse. Who are the people who believe in Salvation by Works? Do you mean Roman Catholics? I'm pretty sure they believe in 'Salvation by the Church' - i.e. you can't be saved outside of the church. The rest has to do with purification from sin, so one can stand before the face of God and not be straw and grass.

Then who would this be? Pelagians? Muslims? It isn't clear to me.

There's a simpler answer than all of the others:

In Sum, why not believe in salvation by grace?

Because you don't just choose what you believe. You believe things because you think they're true. So, even if this argument was valid, it wouldn't be useful, because it recommends a choice that you don't control. The same applies to Pascal's Wager.

I believe that the demographic for your gambit would object on a couple of grounds.

Firstly, they would object to sacrificing integrity in choosing to believe something that one does not actually believe.

Secondly, they would object to your premise:

If you are saved by grace, you should want to serve God as heartily and fully as possible, loving him and your neighbor and doing good works

By those who oppose the view, the by-faith-no-works view is often (mis)characterized as a license to sin. They generally do not accept that good works would be the result of salvation by grace, and thus would not take such a wager, for fear of losing their motivation for good work.

Like @DavidMorton, I come from a sola fide perspective, so this is somewhat speculative.

Here's the Arminian perspective:

Background

First, a little background. Jacobus Arminius was a Reformed theologian who eventually became convinced that Calvin's views of predestination and unconditional election made God the author of evil. His reasoning was that if God controls all our choices and does not give us free will, then even our wrong choices are the result of God's action. A Calvinist may disagree with Arminius' assertion, but that is nonetheless where Arminius ended up when attempting to take Calvinism to its logical conclusion, and that conclusion was not compatible with the biblical teaching that God desires everyone to be saved (1 Timothy 2:4, 2 Peter 3:9).

Arminius argued that God has given us all (Titus 2:11) the grace to follow his will (known as "prevenient grace" because it precedes any decisions we might make), but that we also have been given freedom to go our own way. In other words, all of our wrong choices are fully our responsibility, and God can in no way be considered the author of evil. All of our right choices, on the other hand, are through no merit of our own, but are merely a response to God's grace.

The Grace Gambit

Second, I'm making an assumption. You say this wager is offered to "any who hold to any degree of human participation of works to salvation"; I'm assuming you mean that to "believe in salvation by grace" is to believe in monergistic salvation, i.e., that God's action alone is responsible for our salvation or damnation and that no response of ours makes any difference.

But that's exactly Arminius' point of contention!

If "salvation by grace" means that God has already chosen who will be saved and who won't, then believing in this type of grace won't save us. We have nothing to gain from either the belief or the good works that may follow.

Salvation

If, however, Arminius is right, then God expects a response from us. Believing that God has already made the response for us won't cut it. Nor do our good works save us, if they are not done as a response to God's call.

If Armninius is right, and God expects us to respond to his grace, to give up our will and follow God's, we have everything to lose if we fail to do so.

Therefore the "grace gambit" fails on both sides of the equation.

This is a Latter-Day Saint perspective.

From the Book of Mormon

2 Nephi 25:23 For we labor diligently to write, to persuade our children, and also our brethren, to believe in Christ, and to be reconciled to God; for we know that it is by grace that we are saved, after all we can do.

Nephi is an accepted ancient prophet in the LDS religion. The whole chapter is really quite good and talks of almost nothing except for Christ. Anyways, to most christians this looks really weird. However if you take a closer look at it it makes a lot of sense. As I put in a comment on a question by @eric most people have an all or nothing view on grace and works. But I think that even in the Bible there is a significant amount of evidence that it is by both that we ultimately obtain our salvation. If you asked me if I was saved by grace I would say absolutely. The grace of Christ and the atonement He preformed is enough to save all men. If you asked me if I was going to live with Heavenly Father and Christ again after I died. I would say I hope so but I am not sure yet because I still have a lot to do here on earth and I could screw up royally and not repent of that.

So to get to your logic specifically I believe that you have to have both because they go hand in hand. Grace itself is not enough to inspire you to do good works. I was out looking for opportunities to serve once, when I met a man that said that he was saved by the grace of Christ and there was no service I could do for him. I said that's great for you, and then I asked if he knew of any others that could use some service on his street to which he replied, "I don't know I'm not my neighbors keeper". This man professed to be saved by grace and yet had no desire whatsoever to help those around him. I wish that I could say this is an isolated experience but its not. So I'll join with James in saying that its by works that we show our faith and it is faith that helps us to do good works. They work together you can not have one without the other. Which means the logic behind the gambit is, at least from an LDS standpoint, faulty.

This isn't truly an "answer" to the question so to speak, so please excuse my butting in here. I think it may be helpful, however, for future readers, to do a small deconstruction of this argument from the perspective of a sola fide belief system. I'm still interested in the other perspectives as well.

While logically, the gambit seems to make sense, it makes unclear the entire object of the faith in a very relativistic way. At it's core, the different soteriologies that exist all point, eventually, to a difference in who God is. The soteriology of salvation by faith alone apart from works implicitly assumes that there is a loving God who has provided a way for us to be near him, and has provided it in such a way so that:

1. We are freed from having to do works for salvation.
2. God is declared righteous and the only one worthy of praise.

To have a "fall-back" position is to either be unclear or deny the character of God has he has revealed it through Scripture. In other words, living by the gambit is inherently a lack of faith in the saving power of God via Christ's sacrifice. It's the kind of relativist "soft belief" that is so pervasive today (for which we have Pascal, among others, to thank).

It's the Christianized version of the relativistic worldview, which will claim to believe something, but doesn't believe either it's truth or it's power enough to stand it up in contrast to conflicting beliefs. In other words, it's prideful unbelief masked in believing terms for no true reason other than to allow the one holding the gambit a false sense of security that they've somehow "out-logicked" God, and thus, he can hold God's hand to the fire saying he must save us because of our amazing prowess with finding loopholes.

In other words, it's another sign of depravity.

And I say this with great humility, realizing as I write this that I, sadly, am too often subject to this form of unbelief.