A. This question came via email from a Chicago area reader. It’s a tough market for blackjack players on a budget. A couple of casinos have low-minimum tables with 6-5 pays on blackjacks. Several have no $5 tables at all, and at busy times of the day will have nothing under $25.

Conditions are such that I’m not sure there is a good answer for a $5 bettor. Craps? Even if a $5 table is open, sticking to a $5 wager means pass or don’t pass with no odds and no extra bets, and I’m not sure I’ve met the craps player who doesn’t want at least a few bets working. Video poker? To offset the speed of the game, a $5 blackjack player would have to drop to quarter video poker to stay within budget, and would have to be playing in a market with full-pay games at quarter levels.

One option is just to play less often, but increase your bankroll per visit. If by playing less often you can withstand the risk at $15 a hand, average losses per hour are lower on a $15 game with 3-2 payoffs on blackjacks than at a $5 game with 6-5 blackjack pays.

Nevertheless, I strongly urge that you do not play 6-5 games, and do fill out a comment card, or let a casino manager know you’re choosing not to return because of the 6-5 pays. As long as the seats are filled, there’s no incentive for operators to improve their games.

A. The house edge on all craps combinations is a weighted average of the component bets. When you place the 6 and the 8, you have two wagers with house edges of 1.52 percent. The overall house edge has to be 1.52 percent.

Others have sent me calculations that show a 1.04 percent edge on that combo. Here’s how it goes: In evaluating craps bets, we throw out rolls that push as irrelevant. Rolls such as 2, 5, or 11 do not yield a decision on the 6 or 8, so we disregard them in calculating a house edge. That leaves only 16 rolls that matter: the 6 ways to make 7, the 5 ways to make 6 and the 5 ways to make 8.

If you wager $6 each on 6 and 8, you risk $192 on the 16 rolls. We get $7 in winnings on each of the five 6s and five 8s, for a total of $70. We lose $12 on each of the six 7s for a total of $72. That’s a net $2 loss. Divide that by the $192 risked, then multiply by 100 to convert to percent, and you get a house edge of only 1.04 percent.

Do you see the flaw?

That calculation treats pushes on 6 and 8 as money at risk, unlike any other pushes. When we calculate the house edge on the combination, we have to disregard money bet on 6 when the roll is an 8, or bets on 8 when the roll is 6.

Now the risk becomes $72 for the 12 7s, $30 for the five 6s, and $30 for the five 8s, for a total of $132. It’s still a net loss of $2, but $2 is 1.52 percent of $132 at risk. That’s the correct house edge on the combination.

A. With three Aces and a kicker, it is the correct play to hold the kicker in Triple Double Bonus Poker, where there's a 4,000-coin Jackpot, but not in Double Double Bonus Poker, where the jackpot is 2,000 coins for four Aces and kicker. Dealt Ace-Ace-Ace-2-6, for instance, the average return in 9-6 Double Double Bonus is 62.4 coins per five wagered when you hold just the Aces, and that drops to 59.1 when you hold the kicker, too. In 9-7 Triple Double Bonus, the bigger jackpot more than makes up for that difference.

With low cards, it's similar. Dealt 3-3-3-2-6, in Double Double Bonus the average return is 37.2 coins for holding 3-3-3, but only 33.6 for holding 3-3-3-2. Just hold the three of a kind. In Triple Double Bonus, where we can get 2,000 for four 3s and a 2, average returns are 57.6 for 3-3-3-2, and only 45.0 for 3-3-3. Therefore, in Triple Double, we hold the kicker.

Two pair and a kicker is another matter. Not even in Triple Double Bonus is it worth your while to hold a kicker with a single pair. Dealt Ace-Ace-5-5-2, in 9-6 Double Double Bonus, the average return for a five-credit wager is 9.6 coins when you hold Ace-Ace, and only 7.6 when you hold Ace-Ace-2. Even in 9-7 Triple Double, the higher return comes from holding just the pair, with an average of 10.4 per five credits wagered when you hold Ace-Ace vs. 9.4 for holding Ace-Ace-2.

By holding the extra card, you’re limiting your opportunities to draw four of a kind, or even three of a kind. The occasional big quads-plus-kicker payoff can’t make that up.