Friday, May 9, 2014

Safe or Sorry

 Penrose Impossible Triangle (best source I can find)
There was no specific math goal for today, so that always puts me in mind for number sense, mental math and operational fluency.

I've been interested in push your luck games (Farkle, Zombie Dice. Pig from the Interactive Mathematics Poject..) but those mechanics can be lame for a whole class math game. Students get bored waiting for the turn to come around. Not enough decisions to make. So I thought of a variation that offered a little better opportunity for mental math, and more activity for the players. The game was a moderate success, but the game design discussion at the end was even better.

Safe or Sorry
Dice game for two or more players.

All the players roll a die. Add them up for a total.
If the total is a multiple of 5 –  turn is over, zero points.
You can stay and take that many points, or keep rolling.
Whoever is still in, rolls again and adds the points to your first total.
If the new total is a multiple of 5 –  turn is over, zero points.
After each roll you have to decide:  stay safe and take the points or keep rolling. If the total is a multiple of 5, though, sorry, the turn is over and you get zero points.

Winner is the first player to 150. If more than one player is over 150, they all win.

Example: 3 players: Ann, Bill and CeCe.
Ann rolls 3, Bill a 4 and CeCe a 5. Total 3+4+5=12
Bill stays and scores 12. Ann rolls a 2, CeCe rolls a 6. 12+2+6 =… 20! That’s a multiple of 5.
Score: Ann =0, Bill = 12, CeCe = 0.

Next turn: Ann, 4; Bill, 4, CeCe, 3: 4+4+3 = 11. Ann stays and scores 11. Bill and CeCe roll: 3 and 5. 11+3+5=19. Bill stays and scores 19. CeCe rolls again: 5. 19+5=24. She rolls again: 5. 24+5=29. She rolls again: 6. 29+6 =35! She loses all the points.
Score: Ann = 11, Bill = 12+19 = 31, CeCe = 0.

You have to know when to stop, CeCe!

Pretty bare bones, but it's the end of the year so I want them doing more of the game design work.

I played a game against the class (Golden vs guys vs girls) to introduce it. The main confusion was whether the multiple of 5 was the total on the roll or the total for the turn. Maybe I need better terminology?  It wasn't a persistent confusion, though. The original game was to 100, but they wanted to 150, and that worked pretty well for the playtest.

The mental math level was appropriate and pretty diverse: some adding the single digit dice for some and writing down the two digit sums, mentally keeping the running total, or considering their score + running total.  Having multiple dice to add gives options for summing, the group nature had people doing it in different ways. I saw everything from counting on to efficient fact use (doubles or sum to ten).

The game was mostly engaging. One group couldn't get into it, two groups played a full game then stopped, and four groups played until awwww, time was called. But, interestingly, the discussion afterward was full engagement, even the group that tried it the least. They all agreed that the game was a keeper, even though it needed some work. There was a fair amount of discussion about the zero condition. Some people wanted it to come up more often, others felt it was okay as is. One student suggested, "what about on multiples of 5s and 10s?" which led to a quick but strong class discussion about that. Some students wanted as hard a condition as even numbers. They recognized that the more common the condition, the more risky continuing to roll, the more often you should stop. The strategy discussion was strong; I was surprised that they recognized they were not stopping enough, but the fun of rolling was worth it. Most of the stories they were telling were of the "I got to 147 on one turn! Then 155 for a zero, of course."

One interesting rules discussion was about whether players who were out be able to come back in. At first the majority thought yes, but then someone pointed out that this made the decision to stay or keep rolling less important. That changed public opinion, but there was an interesting suggestion: when someone else opts out you can choose to come back in.

There does need to be a catch up mechanic, because when you're behind, the risky behavior is not enough to get back in. The opt in might be one way to do it. Other suggestions were that the risk should elevate. A really interesting idea was that there should be extra zero conditions the farther they go. One cool idea was that the zero condition should be a multiple of the number of players!

The game could use a context. The best idea the class had might not be suitable for school! "What about, you're a burglar, and you keep doing jobs, but you might get caught and go to jail. That's the zero." I do like that as a pushing your luck context; would it bother teachers to have their students playing criminals? Do you have a better idea for a context?

I think this is how I'd try it for the next iteration, adding in the extra zero condition:
Safe or Sorry
Dice game for two or more players.

All the players roll a die. Add them up.
If the your total for the turn is ever a multiple of 5 – the turn is over, everyone who rolled gets zero points. Now you can take your points and be safe, or keep rolling.
Whoever is still going rolls again and adds the points to their turn total. If the new total is a multiple of 5, the turn is over, zero points.
After each roll, you have to decide:  stay safe and take the points or keep rolling. If the total is a multiple of 5, though, sorry, the turn is over and you get zero points.
But the longer you stay in, the riskier it gets! If the total is over 50, multiples of 3 also give you zero.

Winner is the first player to 150. If more than one player is over 150, they all win.