Some math
Someone should check my math on this one, but this should shed some light on the situation...
According to Super System, the chances of being dealt the following pat hands before the draw are:
A Full House: 693: 1 (.14%)
A Flush: 508: 1 (.20%)
A Straight 254: 1 (.39%)
Therefore, it follows that one opponent will have either a straight or a flush .59% of the time (.2%+.39%)
So, if you hold deuces full of eights, and your opponent must hold one of the three types of hands listed above, he'll hold a boat slightly less than 25% of the time (.14/.59). So you're a little better than 3:1 to have one player beat. In the real world, you're actually somewhat better than that, because A) your opponent may be false carding, and B) since you have a boat it will be harder for your opponent to also hold one because he can't make a boat using deuces and is unlikely to make one using eights.
Now here's where my math is a little shaky... against two opponents in which they both must hold either a boat, a flush, or a straight, I figure you'll have the best hand about 9/16 of the time. However, my math is based on estimates and is certainly underrepresenting your actual chances. In the real world, I put your chances more along the lines of about 11/16 or 11.5/16 (or about 70%) of having the best hand.
I came to this number by creating a matrix. The matrix assumes that each of your opponents will have a straight or a flush 3 times, and a boat once (representing the 3:1 number I arrived at above). Adding up all the possibilites, there are 16 outcomes, 7 of which give at least one of your opponents a full house. However, this method is flawed. As stated above, your chances are better than 3: 1 for each player. Also, with two opponents it becomes more likely that one of them is false carding. It's certainly feasible that the player to your left has a hand like trip sixes, or the player on the button has a hand like trip aces, and has decided to stand pat in hopes of showing down his hand for free.
All in all, I think this adds up to about a 70% chance you are best. It still doesn't prove whether it is better to bet out or go for a check/raise, but I think it does prove that you don't have to be too afraid of a bigger boat.
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