Help me explain basic probability to simple-minded people

[youtalkfunny]

Here's my problem:

The local cardroom has a "high-hand" promotion. Every two hours, the players who've had the highest hand (one each from HE, stud, and Omaha) pick an envelope. Each envelope holds a slip of paper with a dollar amount written on it, either $25, $50, $75, or $100.

The three contestants will often fight over who gets to choose the first envelope, believing that if they let someone else draw first, the $100 may be snatched up, and they would be "drawing dead".

The house, being equally incompetent in this subject, came up with a rule to placate these players--the HIGHEST of the high hands draws first, and so on down the line.

Which, predictably, was met with glee by Omaha players, and dismay by all others.

Players get passionate about this, and I am completely unable to convince ANYONE, player nor floorman, that there is no advantage to be gained by being first to draw.

--I tell them that if that were the case, the person calling a coin toss would have an advantage over his opponent. They agree that there is no advantage in calling the toss.

--I tell them that if that were the case, everyone would want the "one seat" in stud. After all, if he catches a Royal, I'd be drawing dead. They say that's silly, there's no advantage to sitting in the one seat.

--I tell them that if that the chances of the first player picking the BEST envelope are counter-balanced by the EQUAL chance that he will pick the WORST envelope. These two possibilities cancel each other out.

And they nod, and they say, "Yeah, but if he picks the $100..."

Am I not explaining this properly? IS THERE A WAY TO GET IT THROUGH THEIR HEADS???

[BruceZ]

Try asking them how much they would be willing to pay to trade their envelope for the the first envelope. If they say nothing, you've made your point. If they would be willing to pay something, then you sell it to them.

[Ed Miller]

Much more troubling is that some players are much more likely to win than others depending on what game they play. I assume that there are more HE games than stud games, and more stud games than Omaha games. If that's so, then the Omaha players have more to get excited about than just picking first. /images/graemlins/smile.gif

[Ray Zee]

always explaining things to stupid people is a waste of time. but since you asked tell them that picking last is the best. because if no one has gotten the 100 yet you are sure to be the one.

[MMMMMM]

These are the sort of people you should be nodding and smiling with. Encourage them in their misunderstanding. Give Thanks that you are able to play with them regularly.

P.S. Where is this cardroom and what limits do they play?

[brad]

otoh going first has much higher status.

1st animalistic reasons.

also going first ensures chance you might win biggie. (people look at you whatever, where might pay no attention if big prize is picked.)

hey people are petty. no one will admit to the above. they do it 'for the money' heh

[Homer]

Well, these don't sound like people who understand math, but...

First person:

EV = .25*100 + .25*75 + .25* 50 + .25*25 = $62.50

Second person:

EV = .25*(.33*100 + .33*75 + .33*50) + .25*(.33*100 + .33*75 + .33*25) + .25*(.33*100 + .33*50 + .33*25) + .25*(.33*75 + .33*50 + .33*25) = $62.5

And so on...

-- Homer

[Terry]

I'm with the "why bother" guys.

If you feel you must do something, suggest that they have a seperate set of envelopes for each game.

[taxat]

This reminds me of the elections in the 90's that were decided by a coin toss where the opponents had to first draw for the right to call the coin. Of course, it does not make any difference.

http://www.hollandsentinel.com/stories/061398/new_drawing.html

[Cyrus]

That is not a probability problem, it's rather a matter of perception. There are cases whereby one wants to "choose" last, others first. In many cases, however, this is not unimportant. The (real or imagined) ability to pick a sign/tell/mark which would destroy the randomness is the reason behind the rush to choose first in such instances.

In your example, of course, the players are deluding themselves (except if they have found a way to see through the envelopes).

One way to educate your fellow players is by distancing the prizes from the awarding mechanism. Use playing cards. Deal 4 five-card poker hands to 4 players, face down. No player gets to see his hand so all hands remain face down. The awards in the envelopes will be given according to those 4 poker hands' rank (no redraws of cards, etc).

1. Ask if anyone wants to switch his hand with someone else's hand before they all get to see them. If someone does want to switch, ask his why would he want to to do that, when his hand, lying right there in front of him, face down, "might be a straight flush". This should give you an opening to elaborate on the concept of randomness.

2. Alternatively : before the hands are dealt, ask everyone to name a number from 1 to 10. Then add the numbers. Suppose the sum is 26. Deal the cards, have each player turn his hand face up in front of him, let them all glare at all the hands a few seconds, and then switch the hands around 26 times. This should demonstrate that each hand has the same random chance to land in front of anyone. (The randomness is exemplified by the players themselves picking a number at random.) Note that some players might want to go first in picking a number! Have them bid for that right! They should soon realize their foolishness in trying to get an "edge" that way.

3. Alternatively : deal 4 hands not to the players but in front of the dealer. Then have the players choose which hand they want. If two players go for the same hand, have them bid for it! Etcetera. (It would be particularly helpdful when the bidders are found to have been bidding for an inferior hand.)

By the use of playing cards, one gets to have his "probability" to win the highest prize laid out in front of him, as opposed to the illusion of "choice" when you have envelopes.

--Cyrus