Stupid question - War strategy (1 Viewer)

[snooptodd]

Okay, this isn't a poker question or a strategy question, but I'm asking it here nonetheless.

My 5-year-old twins are obsessed with a card game called "Chomp" ... essentially it's war, but the deck has cards with pictures of things that live in the ocean and the bigger the fish wins.

Because the game is mindless, my mind often wanders. I wonder who would be the favorite if the deck were split in different ways.

Imagine you're playing war with a regular deck of playing cards. Playing heads up, with 26 cards each, would you rather have all four aces but have all your other cards be below 9 or lower? Or would you rather have 16 of your 26 cards be face cards with no aces? You could acquire face cards with your aces once play begins, obviously, if you choose the aces, but if you choose to have the face cards, you'd have a big edge in ties and you could get the aces from your opponent that way.

Someone please do the math on this because I don't want to run 100 simulations (which probably wouldn't be a big enough sample anyway).

 

[ChipEnvy]

That would be some intense math! Well above my capabilities, but my gut tells me that the 16 face cards would be the favorite,

 

[H|Q]

have to deal dry hands. Check the results every 100 hands.

I'm sure a simulator could be written for this, but I'm not going to do it. Interesting question though. Also, thanks for the gift idea for the nieces and nephews!

 

[Ben]

Pretty sure the aces would be a huge favorite. If 16 of the other player's 26 cards are face cards not found in the aces stack, the likelihood of early ties is low. And once the aces start grabbing those face cards, it's all over.

 

[bentax1978]

Just spent the last half-hour writing a quick simulator program. Results in a few...

(I may have been premature with my previous thought).

 

[bentax1978]

Ok, just to clarify, do we want the four aces and then the worst remaining 22 cards in one half? Or do we want four aces and then just no face cards in one half?

Not sure there will be a huge difference.



Also, need to clarify a couple rules.

(1) If there's a war, and you don't have enough cards, do you just use the last one in the deck to go to war with?

(2) Do the cards every get shuffled?



FWIW, preliminary results support @Ben's theory that the aces have a decisive advantage, though the face deck can win.

 

[Jimulacrum]

I'm going to make an informal prediction that the aces would crush the paint hand.

This is just from my experience playing War as a kid (okay, and a little as an adult too). Picking up even one ace makes your hand dramatically stronger. All ranks can be won or lost in a tie-breaker, but aces are the one rank that can only be taken this way.

It essentially takes a parlay to win just one ace from your opponent: You have to not only hit a tie, but have an ace among the "dead" cards and also win the tie-breaker. If you have no aces yourself, then the tied rank can't even be an ace, reducing your chances further.

To come back from a hand where you have all the aces and your opponent has none, he would have to hit four such parlays without you catching any yourself.

 

[bentax1978]

I'm going to make an informal prediction that the aces would crush the paint hand.

That seems to be the way this is going on my simulation so far.

 

[bentax1978]

That seems to be the way this is going on my simulation so far.

Based on the parameters I have in place right now, looks like the aces are taking it about five out of every six matches.

So far it looks pretty close to AA vs KK odds in hold'em

 

[Jimulacrum]

Based on the parameters I have in place right now, looks like the aces are taking it about five out of every six matches.

So far it looks pretty close to AA vs KK odds in hold'em

I was about to guess something like 70–75%. Kinda surprising that it's turning up even higher than that.

 

[bentax1978]

I was about to guess something like 70–75%. Kinda surprising that it's turning up even higher than that.

It's coming down a bit, closer to 78% now.

My "code" is terribly inefficient (I'm not a programmer by any stretch), so these simulations aren't super fast. Up to about 500 games now.



Also, FWIW, the average number of hands to finish is about 150/game (stdev around 90)

 

[snooptodd]

It's coming down a bit, closer to 78% now.

My "code" is terribly inefficient (I'm not a programmer by any stretch), so these simulations aren't super fast. Up to about 500 games now.



Also, FWIW, the average number of hands to finish is about 150/game (stdev around 90)

This is why PCF is awesome, love that you actually did this bentax.

Based on my experience playing war, 150 hands is an incredibly low amount to determine an outcome ... seems like the aces win, and win fast. (I'm assuming you mean one turn is one hand, correct?)

My original premise was that aces would have a random mix of 22 cards, 2s through 9s. That way there would at least be the possibility of having some early ties.

 

[bentax1978]

This is why PCF is awesome, love that you actually did this bentax.

Based on my experience playing war, 150 hands is an incredibly low amount to determine an outcome ... seems like the aces win, and win fast. (I'm assuming you mean one turn is one hand, correct?)

My original premise was that aces would have a random mix of 22 cards, 2s through 9s. That way there would at least be the possibility of having some early ties.

You're welcome. Anything to help pass the time a little quicker on a Friday.

I'll need to go back and tweak things a little so that there's a more random mix of the other 22 cards (which should increase the number of early ties quite a bit). We'll see what kind of an effect that has on the results.

When I said hands, it wasn't strictly speaking the number of turns. My counter was counting the number of times cars were awarded to one player or the other. So a war would count as one hand, even if 4 cards were turned.

 

[bentax1978]

My original premise was that aces would have a random mix of 22 cards, 2s through 9s. That way there would at least be the possibility of having some early ties.

As expected, this changed the results by a decent amount. With a mix of cards 2-9 in both hands, there are a lot more ties. Since ties (wars) are essential to the face card deck acquiring aces, this evened things out a bit.

Now we're looking at almost exactly a 2:1 advantage for the aces vs face card hands. I will still caveat the exact numbers a bit since I don't think I have what to do if you run out of cards during a war programmed correctly. Shouldn't have a major impact since at that point the game is usually pretty much over, but still want to mention it.

Also, note that the cards are never shuffled in my simulation. When you win a battle, the cards go to the bottom of the deck. Not sure what's suppose to happen when you actually play.

 

[Jimulacrum]

Also, note that the cards are never shuffled in my simulation. When you win a battle, the cards go to the bottom of the deck. Not sure what's suppose to happen when you actually play.

Interestingly, I find that the "shuffle rules" employed during a game of War can have significant strategy implications.

I grew up playing a version of War where you stack all the cards you win separately and then shuffle that stack before proceeding. If everyone does this consistently, it has no effect on your winning chances.

But if the rule is that you can choose when to shuffle—even under limited circumstances, like you can do an optional shuffle only if your opponent is shuffling—you can actually gain an advantage. Hard to say exactly how large that advantage is, but it's definitely there, and that's pretty good for a game that's otherwise pure chance.

 

[bentax1978]

I grew up playing a version of War where you stack all the cards you win separately and then shuffle that stack before proceeding. If everyone does this consistently, it has no effect on your winning chances.

I recall playing both way in the past, both putting the newly won cards on the bottom of the deck and keeping them separate and shuffling them when you run out of cards.

I don't have time now (I have to try and get something work related done today), but I can look into adding this as an option in the simulation later.

 

[bentax1978]

Also, for shits and giggles, I ran simulations where both decks were evenly divided, and then the two aces were given to one player before the game started. So basically even decks, except one guy gets the extra two aces in exchange for two other non-ace cards. The guy with the 4 aces has about an 88% chance to win under those circumstances.

 

[Jimulacrum]

Also, for shits and giggles, I ran simulations where both decks were evenly divided, and then the two aces were given to one player before the game started. So basically even decks, except one guy gets the extra two aces in exchange for two other non-ace cards. The guy with the 4 aces has about an 88% chance to win under those circumstances.

What about one player getting 3 aces and the other only getting 1?

 

[rowlin]

"Shall we play a game?"

 

[bentax1978]

What about one player getting 3 aces and the other only getting 1?

Looks like it's right around 75%.


I'm checking two aces now, for completeness and as a sanity check.

 

[bentax1978]

I'm checking two aces now, for completeness and as a sanity check.

Turns out, if you start with two equal hands (2 of each rank), you have a 50/50 shot of winning. Go figure!

Average game length increases (as expected) to around 240.


Tweaked a couple other little things that might have causes small inaccuracies, so I'll probably rerun some of the above numbers at some point. I'm guessing no one but me cares at this point, but it's tough to stop once you've started.

 

[snooptodd]

This might be a fun game to play with an auction ... players bid on each card value, so all four aces, kings, queens, etc., starting with the lower values ... or maybe you just distribute the 2s through 7s randomly and bid on 8s, 9s, 10s, etc., all the way up to aces. Playing it 4-5 handed would be cool, because the bidding would start to get out of control for the kings and aces.

 

[bentax1978]

This might be a fun game to play with an auction ... players bid on each card value, so all four aces, kings, queens, etc., starting with the lower values ... or maybe you just distribute the 2s through 7s randomly and bid on 8s, 9s, 10s, etc., all the way up to aces. Playing it 4-5 handed would be cool, because the bidding would start to get out of control for the kings and aces.

Just to bound the problem, if you equally distribute the cards between 2 and 8, and then give one player all of the 9's, 10's and Jacks and the other player the Queens, Kings and Aces, how often do you think player one can pull off the upset?

Spoiler: answer

About 5% of the time

 

[JoseRijo]

I just came in to say I used to totally cheat at war with my kids. If they were winning, I'd put aces in my tie piles and purposely lose. If I was winning, I would win the ties. Anything to end it.

 

[bentax1978]

I just came in to say I used to totally cheat at war with my kids. If they were winning, I'd put aces in my tie piles. If I was winning, I would win the ties. Anything to end it.

I don't need a simulator to recognize that this is actually the right answer.

 

[Jimulacrum]

Just to bound the problem, if you equally distribute the cards between 2 and 8, and then give one player all of the 9's, 10's and Jacks and the other player the Queens, Kings and Aces, how often do you think player one can pull off the upset?

Spoiler: answer

About 5% of the time

I accidentally peeped the spoiler while replying, but I was going to say something in the low single digits, like 1–2%. That's a lot of parlays to hit.

 

[Jimulacrum]

I just came in to say I used to totally cheat at war with my kids. If they were winning, I'd put aces in my tie piles and purposely lose. If I was winning, I would win the ties. Anything to end it.

The game to play with children is Go Fish. There are meaningful strategic choices built into the game, and you can glean even more of an edge if your opponent is easy to read (like, say, children). No cheating required.

Bonus: No chance of a game insolently refusing to end, like War sometimes does.

 

[snooptodd]

I just came in to say I used to totally cheat at war with my kids. If they were winning, I'd put aces in my tie piles and purposely lose. If I was winning, I would win the ties. Anything to end it.

This x10000