A. Blackjack side bets do usually have short shelf lives, as you note. Usually, that’s because they have very high house edges. The appeal of larger payoffs than you get on the base game wears thin when you lose hand after hand after hand.

Sometimes the appeal is strong enough that the side bet has a second life, and a third and even a fourth. I’ve lost count of how many times I’ve seen Royal Match come back, including in electronic versions from Shuffle Master, which became SHFL Entertainment, and which is now part of Bally Technologies.

The most common version, used on six-deck games and paying 2.5-1 on any two suited cards and 25-1 for a King and Queen of the same suit, has a house edge of 6.67 percent. About 75 percent of hands are non-winners, and the royal matches come up only about once per 337 hands. Given enough playing time, that’s not enough positive reinforcement to overcome the constant drain on the bankroll, so after casinos use it for a while, it goes on the backburner.

Over/Under 13 also has a high house edge at 6.6 percent if you bet the over, 10.1 percent if you bet the under, and 8.6 percent if you bet the first two cards will total 13. Again, there’s a constant bankroll drain. There’s also a complicating factor: Over/Under 13 can be counted, and in the 1990s there were players who, depending on the count, were skipping the blackjack bet and just playing the side bet. Casinos had to amend rules to prevent that. So you had players being turned off by a bankroll drain and operators being turned off by advantage play.

Today, 21 + 3 seems to have hit a sweet spot. Not every player makes the side bet – in fact, the majority don’t. Those who play get a 9-1 payoff if there’s a pair or better in the player’s first two cards plus the dealer’s up card. The house edge of 3.2 percent is lower than that on most other side bets, and not all that different from the edge hunch players face on the base game – especially if the base game is paying 6-5 on blackjacks.

If I were designing a side bet, that’s what I’d aim for – payoffs high enough to attract initial play, and a house edge close enough to the edge against average blackjack players that they don’t notice the difference..

A. There are 2,598,960 possible hands, in which card order doesn’t matter. Of those, 54,912 are three of a kind. And because there are 13 card denominations, one of every 13 three of a kinds are three 4s, leaving 4,224 possible three-4 hands. Divide all possible hands by the number of hands that include three 4s, and you get 615. Your chances of being dealt three 4s on any one hand are 1 in 615.

For the chances of it happening three times in a row, multiply 615x615x615. There is a 1 in 232,608,375 chance – and yes, that’s 232 million.

That seems very unlikely, and it is. However, millions of hands of video poker are played in casinos every day, and the unlikely will happen as a matter of course. You just happened to be in the right place at the right time to see it.

As for failing to draw the fourth 4 three hands in a row, that’s par for the course. After you’ve seen your first five cards, there are 47 remaining in the deck. If you hold just the three 4s and draw two cards, you have two chances in 47 to draw the final 4, which we can reduce to 1 in 23.5.

That means there are 22.5 chances in 23.5 that you will NOT draw the fourth 4. Given three hands with three 4s, there is an 87.77 percent chance that you will miss on all three.

A. The closeness of the call depends on a couple of things: How much do full houses pay, and is there an extra jackpot if you draw a designated kicker to go with the Aces?

In 10-7-5 Double Bonus Poker, where full houses pay 10-for-1, your average return for a five-coin bet is 50.57 coins if you hold three Aces, compared to a flat 50-coin payoff if you hold the full house.

If you drop to a 9-6-5 or 9-6-4 pay table – all too common nowadays – the average return for holding three Aces dips slightly to 50.26 coins, but the reward for standing pat drops to 45 coins. This no longer is in the realm of close calls.

Make the game 9-6 Double Double Bonus, and the 2,000-coin bonanza for four Aces plus a low kicker takes the average return when holding Ace-Ace-Ace to 63.58 coins, and that towers over the 45-coin full house return.

In a non-kicker game with a high full house return such as 10-7-5 Double Bonus, it ca be a close call, but in games with big payoffs for four Aces with a kicker, breaking up the Aces-up full house is a no brainer.