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Poker and the “Split or Steal” Game

May 26, 2021

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You’ve probably heard about the Monty Hall problem. At the climax of a game show, a single contestant has to make a decision, sometimes concerning goats or cars, which eventually leads to determining the value of a prize they may or may not win. This has been thoroughly examined and is a good example of how your initial guess about the odds, and the best choice, is not always correct.

Another game show ending is the Split or Steal challenge:

This requires two contestants and a prize pool, which they are invited to compete directly against each other for in a type of auction or ballot.

  • Each player gets to secretly choose one of two options, Split or Steal. 
  • Players are allowed to negotiate. There is a sizeable element of trust and/or deception involved.
  • The players are not bound by any assurances they may make during the negotiation.

The players reveal their choice simultaneously and the prize is awarded according to the following rules:

  • Both players choose Split: The prize is divided equally between them.
  • Both players choose Steal: The prize is forfeit and both players leave with no win.
  • One chooses Split and the other Steal: The player who chooses Steal wins the entire prize.

Which would you choose?

Is there a best choice?

Would you rely on your gut instinct during the negotiation and trust your opponent if they “promise” to split?

How does this apply to poker?

As with the Monty Hall problem, this has been studied in depth and there is an “optimal” play. (“Optimal” being the recommended mathematically best expectation.)

But ironically, second guessing the level of game theory your opponent uses has an important effect on how your thought process might go.

  • If you are friendly with the fellow contestant and there seems to be a mutual trust between you, then you might go for Split. But beware! What if they realize you are happy to do that and try to take the whole prize?
  • You might take the view you have come this far and rather than both players leave empty handed, you will offer Split, At least someone gets the prize and hopefully you have half. This Good Samaritan approach may end in martyrdom, though.
  • You might become more mercenary and decide that all or nothing is what you came for, so Steal is the only way to go.

What does the math say?

The math says … always Steal!  

Why is that? Allowing any chance of an awesome prize to be unclaimed seems like such a waste. You ruin the day of your fellow contestant and shoot yourself in the foot at the same time.

In the event you are faced with a completely random or undecided opponent who is equally likely to choose each option, then this is how it breaks down:

  • If you always pick Split, half the time you get half the prize and half the time you get nothing
  • If you always pick Steal, half the time you get all the prize and half the time you still get nothing.
  • Therefore, it is mathematically better to choose Steal against an opponent who is choosing either option about half the time.

Against an opponent who has the same knowledge you now have, you are relying more on intuition.

  • The negotiation is key to deciding whether to go for the cutthroat or the benevolent choice.

Disclaimer: Replay’s recommendation is take each Game Show Finale as it comes, and good luck!

So, how does this relate to poker?

Ask yourself which sort of opponent you want to be against in this type of game. A thinking player who realizes that Steal is the recommended choice? Or a casual player who will simply guess?

Against the thinker, you are really up against it because you might easily return no win, unless you can strike a genuine accord. Against the guesser, you make the best Game Theory choice and accept the result, whatever it may be.

Then ask yourself what sort of poker player is your best opponent. A clued-up, thinking player? Or a guesser who might get lucky from time to time, but ultimately busts — even if it’s not always to you.

Next time you hear someone moan that they don’t like playing against “bad” players, remember that it’s the bad players who make the bad decisions.