(Note: Answers are at the end.)

1. You've made it to the final round of a million-dollar blackjack tournament and there are only two players left, you and tournament pro Kenneth Smith. It's the last hand and you have a commanding lead over Ken with a $49,000 bankroll to his $20,000. There are no maximum betting limits in this tournament and the minimum bet is only $5. Surrender isn't offered. First place prize is a million bucks; second place wins $50,000. You are on the button (meaning, you must bet first, before Ken does), and you have 30 seconds to decide how much you are going to bet. What would you do? Would you:

1. Go all in with a $49,000 bet.
2. Make a minimum $5 bet.
3. Bet at least $1,005 but no more than $8,995.

2. With the million bucks you just won in the blackjack tournament by beating Ken, you decide to play in a one-day blackjack promotion at your local casino. It's a special single-deck game where the dealer stands on soft 17, blackjacks are paid at 3-2 (rather than the deplorable 6-5), and doubling down after pair splitting is not permitted. (A basic strategy player has a very tiny two thousands of a percent edge against the casino in this game.) The maximum betting limit is $10,000. The casino also guarantees that two rounds will be dealt before the cards are shuffled. You join the game with five other players, and start firing away with $10,000 bets on each round. Luckily, you win your first six hands and are up sixty grand. The dealer shuffles the cards, you make another $10,000 wager, and low-and-behold, you and three other table players get blackjacks. There's a lot of whopping and holler going on at the table as the dealer starts paying off all the blackjacks. When the round is over, the floor supervisor comes over and announces that the betting limit is being raised to $25,000, beginning with the next round. How lucky can you get! You're on a hot streak and the casino is letting you increase your bet to $25,000. What would do? Would you make a $25,000 bet in the next round? (Yes or no?)

3. You are playing blackjack in a Las Vegas casino when a new dealer takes over the dealing chores. While she shuffles the cards, you start making small talk with her and find out that she recently graduated from dealing school. It's a double-deck game, and she begins to pitch the cards to the players. However, you notice something unusual. Occasionally, the dealer is unknowingly exposing her hole card (a dealer who does this is known as a "flashing dealer"). She obviously needs to practice her dealing technique but now you are faced with this dilemma. Should you take advantage of her sloppy dealing by playing your hand based on knowing what the dealer's hole card is (which gives you a tremendous advantage)? But what if you were caught taking advantage of this flashing dealer? Would you be accused of cheating? Would you:

1. Stop playing because it's illegal to take advantage of a flashing dealer.
2. Keep playing because there is nothing illegal about taking advantage of a flashing dealer.

1. Because there is such a large spread between the million-dollar first-place prize and the $50,000 second-place prize, it's clear that you should do whatever it takes to wind up with more chips than Ken after the last hand is played. What you definitely want to avoid is a swing, meaning if you lose the last hand and Ken wins his last hand, he winds up with more chips than you do. Therefore, going all in and betting $49,000 would be a big mistake. If you assume that Ken will go all in and bet $20,000, he could wind up with $40,000 if he wins his last hand. Betting the minimum $5 seems OK (even if you lost your hand, you'd wind up with $48,995, which would beat Ken's $40,000). However, making the minimum $5 bet is another big mistake. That's because you haven't covered the possibility that Ken could get lucky and get a blackjack on the last hand (a one in roughly 21 possibility). If that happens, he'd get paid $30,000 for his $20,000 bet and wind up with $50,000, which would be greater than your $49,005 (assuming you won your $5 bet). The optimum bet to make is at least $1005 but no more than $8995. The reason is you will hold back more unbet chips than Ken can attain even if he goes all in and wins. However, you'll also be successful if Ken gets lucky and hits a blackjack. (According to Ken, you'll have more than a 97% chance of winning the million if you bet at least $1005.)

2. Increasing your bet to $25,000 in the next round isn't a smart bet. Why? The fact that four players got blackjacks (in the first round after the shuffle) means that all four aces were removed from the deck and on the next round, there is no possibility of getting a blackjack (and the juicy 3-2 payoff). The fact that you were on a "hot streak" is also immaterial because previous wins (or loses) has no effect on the odds of winning the next hand. (Actually, the smartest bet that you can make in the next round is the table minimum.)

3. I was asked this very question about ‘flashing dealers" on the gambling show. My response was something along these lines. "It's not the player's responsibility to ensure that the dealer is following the casino's dealing protocols. That's the responsibility of the floor supervisor and surveillance personnel. If the dealer is sloppy and exposes her hole card, and that information is available to all the players on the table, there is nothing ‘illegal' about using that information to play your hand." After I gave my response to the question, the show's producer asked the head of the Nevada Gambling Control Board for his opinion. His response was the same as mine; namely, the casino has the responsibility to enforce their dealing procedures, and the player was not doing anything "illegal" by taking advantage of a flashing dealer.