Gamble Plays Blackjack

Now you've really got your work cut out for you, initiate, because your client, Joseph Gamble, is playing Blackjack. Unfortunately, the rules of blackjack require that a bet be placed before the gambler even knows his own cards. Fortunately for you, Gamble is doing reasonably well. Gamble considers himself to be an adept Blackjack player, so he has yet to ask for your advice on any decisions. Every time he wins a round, he turns to you comments something along the lines of "see, I know what I'm doing," or "I told you I'm a good Blackjack player." You notice that he says nothing when he loses, and seems to forget all about it. You're worried he might be suffering from the effects of confirmation bias, or the tendency to only remember information that supports our beliefs, and to interpret other information to support those beliefs as well (Nickerson, 1998), but you decide to keep that information to yourself, for now.

Finally, Gamble seeks your advice. He excitedly informs you that he is on a winning streak. He has won that past four rounds, and now, since luck is on his side, he wants to make a large bet. He reasons that he is a good blackjack player, and can tell when he's on a winning streak. He has a good feeling about the next round, and since the last few rounds have been going well, the next one is more likely to as well. What do you tell him, should he make a large bet or a conservative bet?

Large

Conservative