hi, in the last hebrew webinar we got the bowling activity

__https://danielkline94.github.io/OneOrTwo/__

its a really nice challenge...

i found the strategy of winning when the rule is "the one who takes the last one wins"

but regarding the other option, when the last one loses.. i'v been trying for hours:(

its there a relatively simple strategy for winning this case?

tried to make a table with all the posibilities, but when its over 7 it gets too complicated.

i know nim games often analysed with binary numbers, but i was wondering if i can do without it this time..

thanks!

שלום גלעד!

I see you are starting with small numbers and extending. That's an effective strategy here and in solving many problems. There are two ways to start small here: gameplay begins with few total dots, and a give game has few dots left. Have you thought about both of these?

hi, sorry for the late response..

yes, i tried to analyse every situation starts from 1

i got the strategy till 6, but not when there are mote than 6 pins.

i tried to split them into groups but couldnt find any rule there.

i will appreciate a direction, ot at least the info whether there is a solution to it?

thanks alot,

Gilad

Hi Gilad. I'm new to this game, so I'm figuring it out as well. You might try comparing

last one winsandlast one losesstrategies for a simpler game: only take from one end, never in the middle. Specifically, how are the strategies between the two games similar or different early in the game and late in the game.thanks steve:)

i figured out the last one wins..

i tried some similar strategies here, or to seperate them into certain groups, but it looks like it needs a different one.

i hoped someone from jrmf might tell wethere there is a strategy at all. i found out how to win till 6' but after that the variables become too many, i will be happy to hear from you if and when you figgure this out..

all the best.

Games where you flip who wins at then end are called misere games, and they usually have similar strategies to regular games.

Hi Gilad,

You're right that unlike the "last one wins" game, the "last one loses" game doesn't have a nice, elegant answer (at least, not one that I know of yet!). The variation was included as an extension for people to explore and also to demonstrate just how different the original and misere versions of this game are. If you do find out anything interesting about this variation, we'd love to hear about it, but if you're interested in exploring some extensions with pretty solutions, here are two of my favorites:

1) 2-dimensional version: Create an nxm grid of dots. Players can either take 1 dot or 2 dots that are vertically or horizontally next to each other. The player who takes the last dot wins. Who has a winning strategy?

2) Given n dots, you've been able to find a winning strategy for the "last one wins" variation. Given n dots, can you find

allstarting moves that allows player 1 to win? For which n are there many winning starting moves? For which n are there few winning starting moves?thank you very much daniel!

i have been sitting for hours trying to figure this out, thoght i was missing something. at least now i know i can let go a little:)

and thanks for the other 2 extensions, i really liked the first one..

all the best and good luck!

gilad

Hi Gilad,

Well, it took some perseverance, but I believe I'm up to speed on last-wins for n dots and nxm dots. I have also solved first-to-take-wins! ;-) I definitely benefitted by Daniel's hint that one may not need to fully analyze all positions of a game to find a strategy.

Have you tried this problem? Two players take turns placing round coins on a round table; last placement wins. Does your strategy work for coins of any other shapes?