WAR Variation

Yes, I know that you have to be bored out of your bleepin mind to play WAR but here is the variation:

The bet is $X per card, player posts $X * 5

You are dealt five cards

You can arrange the cards in any order that you see fit, after which you place the cards face down in front of you.

The dealer arranges his hand Highest to lowest.

You play WAR by flipping over your cards, top to bottom, in the order that you set them as the dealer flips over his cards one at a time.

Dealer wins ties

Modification: Cards that beat the dealer by 1 rank is a push.

Player is payed double the initial wager ($X * 5) if he wins all five hands.

Player is debited or credited after all five hands have been played.

It feels like a pretty even wager but who knows...

My thoughts on setting hands:

If I set my hand highest to lowest as the dealer does then my expectation probably becomes more negative; if we are both dealt A's and J's then it is likely that these cards will both be in slots 1 & 2 and dealer will win the ties.

On the other hand, if I don't set my hand highest to lowest then how am I going to sweep all five hands?

The first piece of strategy is to always put 2 against the dealer's' highest card, since it is going to lose at any place anyway :)

Worst-case Scenario Strategy

I ran a simulation of 10,000 random hands. For each hand, I ran all 120 combinations of the 5 player cards versus the dealer's set hand of high to low. I reported the best score from all 120 plays, and what the "worst" ordering was for that score. For each combination, I wanted to see the best result from the "worst" play.

First, the breakdown of scores:
0 wins: 37
1 win: 428
2 wins: 1569
3 wins: 3173
4 wins: 3587
5 wins: 1206

For each score, a breakdown of the hand rankings follows. Dealer always ranks cards 54321 (high to low).
0 wins (1 combo)
Any: 37 /37

1 win (1 combo)
12345: 428 /428

2 wins (2 combos)
12345: 864 /1569
12354: 705 /1569

3 wins (5 combos)
12345: 862 /3173
12435: 455 /3173
12453: 737 /3173
12534: 735 /3173
12543: 384 /3173

4 wins (14 combos)
12345: 350 /3587
13245: 323 /3587
13425: 243 /3587
13452: 297 /3587
14235: 261 /3587
14325: 207 /3587
14352: 261 /3587
14523: 337 /3587
14532: 254 /3587
15234: 301 /3587
15324: 214 /3587
15342: 157 /3587
15423: 221 /3587
15432: 160 /3587

5 wins (42 combos, 40 omitted)
12345: 25 /1206
54321: 28 /1206
(Of the other 40 combinations, the results varied from 16 to 37 wins)

Synopsis
The only unique ranking of cards that is common to all score levels is 12345, low-to-high against dealer high-to-low. In fact, is seems to do best for any number of wins except 5.

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Best-case Scenario Strategy

I ran a simulation of 10,000 random hands. For each hand, I ran all 120 combinations of the 5 player cards versus the dealer's set hand of high to low. I reported the best score from all 120 plays, and what the "best" ordering was for that score. For each combination, I wanted to see the best result from the "best" play.

First, the breakdown of scores:
0 wins: 55
1 win: 478
2 wins: 1608
3 wins: 3281
4 wins: 3407
5 wins: 1171

For this system, I am listing a small selection of rank-orderings that resulted in different scores.
25431
3 wins: 250
4 wins: 177

45312
1 win: 54
2 wins: 34
3 wins: 91
4 wins: 200

45321
3 wins: 290
4 wins: 184

54321
0 wins: 55
1 win: 79
2 wins: 187
3 wins: 528
4 wins: 1477
5 wins: 1171

Synopsis
It seems that 54321 is the best ordering with the most variety of wins. There are other combinations that could result in these wins, but 54321 was the "best" combination of those choices.

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12345 vs. 54321

I ran a simulation of 10,000 random hands. For each hand, I ran 2 combinations of the 5 player cards versus the dealer's set hand of high to low. These 2 combos are 54321 (play like the dealer) and 12345 (opposite the dealer, low to high). The number of hands won will be listed for each combo, and out of the 10,000 hands, how many times each combo did better than the other.

54321 (like dealer) wins
2784
12345 (anti-dealer) wins
4311
Equally good
2905

Accounting for x2 win for 5 wins:
54321 (like dealer) wins
4012 units
12345 (anti-dealer) wins
4346 units

What about 15432?
Guarding against the high card with your low card seems like a sound strategy. Playing it against 12345 and 54321 results in:

15432 (guard vs. dealer) wins
3233
54321 (like dealer) wins
1180
12345 (anti-dealer) wins
1265
2 or 3 tied for 1st
4322

Accounting for x2 win for 5 wins:
15432 (guard vs. dealer) wins
3258 units
54321 (like dealer) wins
1290 units
12345 (anti-dealer) wins
2385 units

Synopsis
Looks like playing 15432 (low card, then highest to 2nd lowest) is the best bet.

I can't say I understand this report, but what buffles me most are two things. First, how come the "best of the worst" result (39493 total wins, counting 5 twice) is worse than the "best of the best" one (38875). And second why there are so many more "5 wins" than "0 wins", they are almost symmetrical (5 wins for player is 0 wins for dealer), except the dealer wins ties, so, if anything, the difference should be the other way around).

And also, what are "combos", and why there is only 1 with 0 wins? I am pretty sure, I can think of a situation where more than one arrangement looses all five bets.

Quote: weaselman

I can't say I understand this report, but what buffles me most are two things. First, how come the "best of the worst" result (39493 total wins, counting 5 twice) is worse than the "best of the best" one (38875). And second why there are so many more "5 wins" than "0 wins", they are almost symmetrical (5 wins for player is 0 wins for dealer), except the dealer wins ties, so, if anything, the difference should be the other way around).

And also, what are "combos", and why there is only 1 with 0 wins? I am pretty sure, I can think of a situation where more than one arrangement looses all five bets.

Yeah, I know, it's difficult to understand. I don't know if my brain was quite fully functioning when I tried to cobble it all together.

There are very few "0 wins", because all 120 possible combinations of player cards made 0 wins. (All player cards were equal to or lower than the lowest dealer card). There are a decent number of "5 wins", because you only need to be able to beat each individual dealer card with one of your individual player cards; All player cards need not be higher than the highest dealer card.

What are the combos?
54321 means ordering your hand highest to lowest, just like the dealer. (5 = highest card, 1 = lowest card).
12345 means ordering your hand lowest to highest, opposite of what the dealer does.

For worst-case scenario, only the worst ranking of cards was shown. So, if the report says:
4 wins: 14235
This means that 4 wins was the best these 5 cards could do, and 14235 was the "worst" way to rank them. Combinations such as 24135, 45312, or 54321 might also win 4 times. The "worst" way to rank means putting lower cards against dealer's high cards.

I am not sure where you are getting the numbers 39,493 and 38,875. There are only 10,000 hands being played.

I hope this clarifies a few points. Thanks for replying!

Quote: weaselman

I can't say I understand this report, but what buffles me most are two things. First, how come the "best of the worst" result (39493 total wins, counting 5 twice) is worse than the "best of the best" one (38875). And second why there are so many more "5 wins" than "0 wins", they are almost symmetrical (5 wins for player is 0 wins for dealer), except the dealer wins ties, so, if anything, the difference should be the other way around).

And also, what are "combos", and why there is only 1 with 0 wins? I am pretty sure, I can think of a situation where more than one arrangement looses all five bets.

Sure - if the player has 3 4 4 6 6 and the dealer has 5 cards 7 and higher, all 5! arrangements are 0s. But 10k samples may not have hit one of those; after all, there are about 9 orders of magnitude more hands than that.

Thank you Dween, your posts are both a surprise and appreciated =)

"First, the breakdown of scores:
0 wins: 55
1 win: 478
2 wins: 1608
3 wins: 3281
4 wins: 3407
5 wins: 1171"

It looks to me like the ability to arrange your cards throws the game heavily in favor of the player even with ties going to the dealer...this is unexpected.

I wonder if adding the a rule that a card that beats the dealer by 1 rank is a push might level things a bit ie

Dealer has a Q: Players Q loses, K (1 rank higher) pushes, A wins.

Dealer has a 7: Players 7 loses, 8 (1 rank higher) pushes, 9-A wins.

never mind, wrong thread :)

Making cards that beat the dealer by 1 rank a push seems to have leveled the player wins off considerably.

I'll set my hand 12543 unless: 5 is an Ace, 4 is Queen+, & 1 is a 9+ in which case my hand is set 54321.

I really have not even played a thousand hands yet so I really don't know what's what, I am going off of Dweens numbers to figure out what I should do =)

Under the rules that a dealer wins ties and beating the dealer by one rank is a push, how would I go about calculating the odds of winning five in a row?

I removed 2's, 3's, & 4's

Dealer wins ties and gives player an exchange token

If player has 5 tokens on the table then dealer will not award further exchange tokens

Player may use up to 5 tokens to discard an equal number of cards for the same number of cards from the deck.

Player beats dealer by 1 rank is a push

Game is played the same:

Player antes $X * 5 cards

Dealer arranges his hand highest to lowest

Player arranges his hand however he wishes

Cards are turned over in the order they are set

Player wins $X for every card that beats the dealer by 2 ranks

Player loses $X for every card that is equal to or less than the dealers rank.