War blackjack indicies

[Blackriver]

Good breakdown of the side bet here
http://wizardofodds.com/games/war-blackjack/

Before you get your second card the dealer takes your side bet unless your first card beats their up card. Otherwise the dealer matches your bet. you can keep your winnings or parlay the winnings onto your blackjack bet before you see your next card.

Here are the expected values of parlaying wins


Expected Value Table after Two Cards
PLAYER
CARD DEALER CARD
2 3 4 5 6 7 8 9 10 J Q K A
2 Loss Loss Loss Loss Loss Loss Loss Loss Loss Loss Loss Loss -0.477328
3 -0.067072 Loss Loss Loss Loss Loss Loss Loss Loss Loss Loss Loss -0.493467
4 -0.081435 -0.043845 Loss Loss Loss Loss Loss Loss Loss Loss Loss Loss -0.509968
5 -0.094434 -0.056269 -0.013914 Loss Loss Loss Loss Loss Loss Loss Loss Loss -0.525235
6 -0.102975 -0.056679 -0.007415 0.042483 Loss Loss Loss Loss Loss Loss Loss Loss -0.534153
7 -0.065916 -0.021684 0.025496 0.074316 0.125486 Loss Loss Loss Loss Loss Loss Loss -0.543463
8 0.03422 0.070862 0.109038 0.148831 0.190361 0.162702 Loss Loss Loss Loss Loss Loss -0.486622
9 0.096481 0.128206 0.16138 0.196182 0.231257 0.185002 0.117605 Loss Loss Loss Loss Loss -0.390236
10 0.22864 0.252115 0.276744 0.302689 0.329076 0.301068 0.241753 0.160387 Loss Loss Loss Loss -0.226097
J 0.22864 0.252115 0.276744 0.302689 0.329076 0.301068 0.241753 0.160387 -0.006345 Loss Loss Loss -0.226097
Q 0.22864 0.252115 0.276744 0.302689 0.329076 0.301068 0.241753 0.160387 -0.006345 -0.006345 Loss Loss -0.226097
K 0.22864 0.252115 0.276744 0.302689 0.329076 0.301068 0.241753 0.160387 -0.006345 -0.006345 -0.006345 Loss -0.226097
A Loss Loss Loss Loss Loss Loss Loss Loss Loss Loss Loss Loss Loss

i think at high counts your eV goes up a lot and the 7v3 and 6/5v4 become positive. Are aces even good for this side bet? It makes hands more unpredictable, reducing the benefit of getting to parlay while you have an advantage. The minimum adjustment from Hilo would be to ignore aces and deuces. I would guess aces and deuces are both pretty bad tho, maybe worse than 5s and 6s. So maybe use a balanced count of a-4 vs tens or else use a-6 vs cards 8+

[muckz]

The ace is on the negative EoR side but heavily leaning toward a neutral card. This could be explained by simple probabilities in dealing procedure in that if you do not receive an ace as your first card the dealers chances of receiving an ace increase.
If you want to beat the entire game, you need to use an advanced count for use in both the blackjack game and sidebet.

The game is riddled with dealer errors, disliked by casino staff and far less popular than other sidebets.

[moo321]

Wait, you have a side bet which is basically casino war (pretty bad), but if you win you have the option to add to your bet based on one player card and one dealer card?

The question is, what is the value of the option? How frequently do you have a +EV bet, and how much EV can you pick up? Does this change by count?

My guess is that the house edge on the side bet is always higher than the value of the option to "cap" your bet, but someone should sim it.

[Nyne]

Moo, here's the Wizard's page on it. http://wizardofodds.com/games/war-blackjack/

If you want to figure out count based deviations from the basic parlaying strategy, you would need to figure out the EV by count and by player first card/dealer upcard pair. Since the player Ace never wins the war bet, it is irrelevant. The 4-10 upcards have almost exactly the same EV vs. each dealer upcard as if you had a 2 card hard total of that number. So player 1st card 7 vs. dealer 2 up is worth the same as a player 2 card hard 7 vs. dealer 2 up, for example. That's not strictly accurate, but it's so close it's fine for this purpose. So all you need to do is figure out at which TC each matchup becomes a player edge, and parlay any time you have the advantage. I haven't done it myself, so I can't say if it makes the game playable or not.

[Dog Hand]

<snip>The 4-10 upcards have almost exactly the same EV vs. each dealer upcard as if you had a 2 card hard total of that number. So player 1st card 7 vs. dealer 2 up is worth the same as a player 2 card hard 7 vs. dealer 2 up, for example. That's not strictly accurate, but it's so close it's fine for this purpose.<snip>

Nyne,

Did you consider the possibility of splitting? 4-4 vs. 6 is much higher EV than, say 5-3 vs. 6, since with DAS you'd split the 4's.

Dog Hand

[Nyne]

Very good point, no I did not. However, 44v6 cannot come up for the parlay strategy since you have to win the war bet first and 4v6 is a loss. However, for 6v[2-5] this will impact the evaluation, as well as for 8v[2-7], so for those you will need to do a little more work. In fact, I see now that I also didn't factor in the availability of doubling after you receive the 2nd card. For example, with a 6v4 matchup, you can draw an A, 3, 4, or 5 to get a double down hand or a 6 to get a split hand. So...scratch what I said above. Doh!

[moo321]

I don't think this is going to be vulnerable to any counting system. Casino war certainly is not vulnerable to counting, and a heavy or light deck is equally likely to result in strong/weak first cards for both player and dealer.

On the other hand, sequencing, next card, and other methods could produce powerful results for this bet.

[Blackriver]

The house edge from wiz says war is 2.8% and war bj is 1.1% (this includes the .5% from playing bj)

so the parlay is worth +1.7% (= 2.8 - 1.1)

If half the time your parlay goes through a .5% house edge so (1/2)*0.5%, .25% of the 1.1% is from the blackjack

[Nyne]

[edited to remove incorrect EOR data]

The house edge from wiz says war is 2.8% and war bj is 1.1% (this includes the .5% from playing bj)

so the parlay is worth +1.7% (= 2.8 - 1.1)

This is different than Casino War because if you tie on this game, it's a loss. You don't get to go to war. So if you didn't get to parlay the bet, you'd be playing at a -7.4% edge. The parlay option gets back most of that.

[Three]

The war bet is not subject to counting as the dealer has an equal likelihood to get the high card in the pair of cards considered at all times. The parlay strategy really isn't going to have many deviations. If the matchup is plus EV you parlay. The biggest potential for gain is the relative sizes of your war bet to your basic bet. The edge from the parlay matchup will change with the count. But since it is based on you having only one card the parlay play is limited. Obviously in a high count the T is a great first card to parlay especially with lots of excess aces. Lots of excess aces would also mean lots of auto losses and auto wins. You would never parlay against the ace.

The odds of getting a parlay hand are best when there are lots of 4, 5 and 6's in the deck and/or lots of 7, 8, 9 and T's in the deck. obviously lots of the former is not good for blackjack. Counting ranks that are best for the parlay for the most likely cards:
T: A, T and 9.
9: A , 9, T and 2
The 9 and T are 16 of your 26 parlays.

You are counting the A, 2, 9 as side counts and 3-6 v T as a main count (Hiopt I). I would think the biggest war bets would be in a deck rich in A, 2 and 9 or a partial combination of these cards in a high Hiopt I main count. You would get the strongest parlays with the highest EV for the parlays. Sims would need to show whether this was an advantageous combination bet or not. I could be way off but this is where I would start looking for an added advantage.

[moo321]

The ace is considered low for war purposes. That completely kills this bet, because you don't have the option to parlay onto(far and away) your most valuable first card. There's basically not going to be a meaningful TC where the war+bj combination becomes positive.