Texas Hold Em Side Bet

This question was previously posted on the Wizard of Odds site:

"Last night a player offered me a side wager in Texas Hold 'em. He said that at least one face card (or any three ranks) would appear on the flop and offered even money? Should I have accepted the bet?

The number of ways you can choose 3 cards out of the 40 non-face cards is (40*39*38)/(1*2*3) = 9,880. The number of ways you can choose 3 cards out of 52 is (52*51*50)/(1*2*3) = 22,100. So the probability of not getting a face card is 9,880/22,100 = 44.71%. Thus, the probability of getting a face is 55.29%. His side of the bet had a 10.58% advantage. April 3, 2005"

My question is, "How much does knowledge of your hole cards change the advantage?" My rough figuring has a 3.3% advantage if you have one face, and a small positive expectation (.4%), if you have two faces. Can anyone confirm? I am not certain where the knowledge of your own two cards comes into play. Do you reduce the "universe" to 50 in both cases where you have one or two face cards?

I'm rewording the question so it makes sence (to me atleast).
Random person with no hole card info wants to bet you that atleast one face will happen on the flop. What will your advantage be based on your hole cards?
You have two faces: .82 % (You would win 82 cents per $100 bet on average)
You have one face: -6.74% (You would lose $6.74 cents per $100 bet on average)
You have no faces: -13.92 % (You would lose $13.92 cents per $100 bet on average)]
Of course I may have made a mistake somewhere.

Quote:

Do you reduce the "universe" to 50 in both cases where you have one or two face cards?

Yep. and change the 40*39*38 to 39*38*37 if you have one face and 38*37*36 if you have no face cards.

Your calculations are correct. You just need to subtract the losses from the wins to get the better's advantage. Knowing that there are 50 cards left, there are 19,600 possibilities (50 x 49 x 48 / (1 x 2 x 3)) of cards to be drawn.

Face	Non-Face	Non-Face combos	Non-face %	Expected loss
2	0	9880	50.408%	-0.816%
1	1	9139	46.628%	6.745%
0	2	8436	43.041%	13.918%

Of course, if you look at your cards and the player you are betting with also looks at theirs then the player can make the bet based on their hand. The table below shows the combined expected losses based on the composition of both hands. In this case there is (48 x 47 x 46 / 6) 17,296 combinations of cards that can be drawn.

# of Player	# of Your	# Non Face	# Non-Face	Non-face	Expected
Face Cards	Face Cards	Remaining	Combos	Percent	Loss
2	2	40	9880	57.123%	-14.126%
1/2	2/1	39	9139	52.839%	-5.678%
0/1/2	2/1/0	38	8436	48.774%	2.451%
0/1	1/0	37	7770	44.924%	10.153%
0	0	36	7140	41.281%	17.438%

If the player making the bet with you has no face cards, then the bet is always in their advantage.