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tedd's avatar

Am I missing something in the odds of the card game "war"?

Asked by tedd (14018 points ) July 26th, 2011

So I was in Vegas last week on work training and a mini vacation with my girlfriend. At the casino’s I didn’t really plan on gambling much since I know I suck at the card games and I know the slots are a rip-off. I did want to gamble a bit though (being in Vegas and all) so I set aside some money to try my luck at Black Jack, and I studied up on the rules and what not.

Well to my surprise while looking around the casino’s, many of them offered a table game called “Casino War.” For those not familiar with the card game war, you take the deck of cards and split it evenly among those playing (usually two). The players then each lift their top card at the same time, and the player with the higher face card “wins” both cards to go into the bottom of their deck. So for example if I’m playing you and you flip a 10 and I flip a Queen, I “win” and put your 10 and my Queen on the bottom of the deck. Casino War works basically the same way, except rather than playing for the cards in play, you’re playing for whatever you bet (min $10, max $1000), and the bet is decided every “hand” of War.

I was stunned that a game involving no strategy would be there, and moreover as best I can tell the House has no “advantage” in a game of war. I thought about it long and hard and all I could come up with was 50/50 odds. Whats more, if you got a “double war” (where you played war and got the same card a second time) you won, and the house doubled your winnings.

SO I used a strategy I had been told for Black Jack. Basically in Black Jack you’ve got a good 30–40% chance of winning any given hand, so you hedge your bets and every time you lose you double your bet on the next hand. The concept being if I lose 10 on one bet, but I win 20 on the next bet, I’ve made back all I lost and what I would’ve won on the last hand, plus I won the next hands worth. “Essentially” you can’t lose using that method, so long as you’re always able to double your bet (the problem coming in when you’ve lost 4–5 hands in a row suddenly you have to have a few hundred dollars to double it). I copied this same strategy to War, assuming my odds to be roughly 50% on any given hand.

Well I sat down with $50 in chips and started playing. In less than 10 minutes I was handing my g/f $25 chips off the table, so that I could “draw a line” and not lose my winnings. Quickly I had handed her the $50 I started with, and then kept adding more. At one point I was up to almost $500. What eventually got me was that once I had enough money to double my bets for 3 or so hands, I would up my minimum wager. So where I started at $10, I eventually moved up to $15 and so on until I reached $30 per hand. Eventually I lost enough hands in a row that I simply didn’t have the money to keep doubling, and I finally lost all of my money that was still on the table. When it was said and done I turned to my g/f who was now holding $300 in $25 chips. Which I cashed in for a $250 profit in about 40 minutes of play.

I would play 2 more times, making $30 once, and breaking even the other. Both times though I found myself at least $150 up at one point.

So my question is basically this… what on Earth are the Casino’s thinking? Now granted I didn’t see anyone else at the War tables playing with the doubling strategy I was using, but even so the odds are still 50/50 right? Why on Earth is a casino giving you a game with even odds? Are they banking that greatly on you just blowing the money elsewhere in the Casino? Am I missing something and its not actually 50/50?

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14 Answers

rebbel's avatar

I am sorry, but i can’t help you with the numbers and percentages, it simply goes above my head.
The only thing I can come up with is that, no, it probably isn’t 50/50.
Or it is and they think: “Okay, we gain nothing, we lose nothing, no big deal (unlikely).
Or it is 50/50 and they think: “The people that win some cash will feel triumphant and most probably will try their hand at other games in our casino and lose their profits anyway. ”

funkdaddy's avatar

The advantage comes in when you go to “war”... you double your bet and only get paid on your additional bet while risking both.

A more complete explanation along with the percentages.

josie's avatar

See @funkdaddy Add the fact that unless you go to “war” the house gets half your bet. Going to “war” gives the house another shot at your money, but your original bet is a push, no win.The house gets two chances to win, you only get one.

Play the odds bet on the Pass line at the Craps table. Best bet in the house.

tedd's avatar

Still, this doesn’t seem like that good of a deal for the House. Even if not exactly 50/50, its surprisingly good odds.

funkdaddy's avatar

@tedd A 2% house advantage means whatever money is put on the table, long term, 2% will go to the house.

Good odds or no, all they need is for people to keep playing.

PhiNotPi's avatar

They would have that game mostly as an encouragement to play other games. The odds are 50/50.

Also, there is a major mathematical flaw in your doubling strategy (called the Martingale betting system). As long as there is a maximum bet, the strategy does not have an advantage over pure chance. This is because the large chance that you make a small gain perfectly balances the small chance that you will make a large loss. If you have infinite money to bet, then the strategy would work, but since you don’t, it doesn’t offer any advantage.

tedd's avatar

@PhiNotPi Yah not having infinite money to bet was ultimately my downfall (that and upping my lowest bet marginally as I went on).

But really, what are the odds that you lose say…. 10 hands in a row? Or even just 5 hands in a row?

Its not fool proof by any means, but it worked pretty well for me.

PhiNotPi's avatar

@tedd If you don’t believe me in the fact that the Martingale system doesn’t work, read the wikipedia article, it has all of the math in it, and would be too hard to explain on Fluther.

The odds of losing ten games of war in a row would be 1/1024.

Assume that you had infinite wealh, and would play until you win, but could not play more than ten rounds. If you won within the ten rounds, you would make a profit equal to your original stake, $10. If you do this whole process 1024 times, chances are you won 1023 times, for a profit of $10230. Chances are you lost 1 time. That one time, your losses would be $10230, exactly what you had gained. If you place any limit on the Martingale system, it fails to inprove your chances of winning.

tedd's avatar

@PhiNotPi I see what you’re saying, but you are assuming (falsely) that I am going to play the game 1024 times, and it will turn out exactly 1/1024.

For example, if I flip a coin an infinite amount of times, it will eventually trend towards a 50/50 ratio of heads vs tails…. but if I flip it 100 times only, it may come out to be 46/54 or 51/49.

The “Martingale” system is not exact, nor is it without chance of failure, but its a heck of a lot better odds at a casino game than just playing your chances. The entire time I played I don’t think I lost more than 3 hands in a row…. if we took that all the way out to ten hands in a row, which is less than a 1 in one thousand chance of happening, I would need $10240 to double my bet ten times in a row, and win $10 on every hand played. I like my odds of not being 1 in over one thousand at that. In fact I like my odds at not losing more than 5 hands in a row.

PhiNotPi's avatar

There are a lot of sources sayng that the Martingale system doesn’t improve your chances above random.Link 1 Link 2

tedd's avatar

well i mean take the name of the system out of it and just do the math. If I play 1 hand, I have roughly a 50/50 chance of winning . If I play two games my odds of winning at least one of them are roughly 3 in 4. Up that to three games and the odds go up to 7 in 8, and so on and so forth. Now obviously I don’t know exactly which game I will win and which I will lose, and obviously the system is not 100% fool proof (I could theoretically lose 100 games in a row). But if you play even just 2 games, the odds increasingly favor you to win at least one hand, which by doubling your bets is all you would need to win back everything you’ve lost and make a steady $10 per hand.

PhiNotPi's avatar

Even though the odds increasingly favor winning, the amount that you would lose increases as well.
A 75% chance of winning $10 balances out the 25% chance of losing $30.
75% * 10 – 25% * 30 = 0

tedd's avatar

I don’t think you can just multiply chance by money like that. The amount I would lose has no effect on the odds that I would win.

PhiNotPi's avatar

True, but it does have an effect on your expectation value, which is what governs what you will win in the long term. And yes, you can multiply money like that.

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