Match Play Strategy

The casinos I play in are typically smaller 'cardrooms' that don't have many options when it comes to promotions. As a result, a significant amount of their promoting comes from giving players club members match plays every time, or nearly every time they show up. To take full advantage of this, I've long looked for an optimal match-play strategy. A year after I first started looking, I gave up and developed my own crude set of standard deviations. The calculation is extremely crude (see below), but I would expect that it still improves on basic strategy, albeit probably not optimally.

---------------------RESULTS---------------------
Here are the strategy deviations I found (rules are 6D, H17, DAS, RSA).

11 v A: Hit (for a .01 increase in EV)

Soft 13 v 5: Hit (.03)
Soft 15 v 4: Hit (.01)
Soft 18 v 2: Stand (.02)
Soft 19 v 6: Stand (.10)

2,2 v 8: Split (.01)
3,3 v 8: Split (.04)
6,6 v 7: Split (.01)
7,7 v 8: Split (.08)
9,9 v A: Split (.03)

The last one is the most surprising. Splitting 9's versus an Ace! Basic strategy favors standing for an EV of -0.219502 versus splitting with an EV of -0.240949. However, my match play strategy favors splitting with an EV of 0.19881375 versus standing, with an EV of 0.170747.

As an added bit of trivia, the hand with the most benefit of a match (excluding naturals for which the match wins 96% of the time--when there is no push) is 20v8. You can expect to receive 89% of the value of the match if you are dealt this hand. Presumably this is because it is the best possible non-natural hand. Conceptually this makes sense. The dealer cannot beat or even push you without drawing two cards. There is a 46% chance that the dealer will deal a single card and stop. Another 38% of the time the dealer will draw to a stiff and likely bust or still fail to beat/push 20. You may note that the EV of this hand is actually .79 yet I say that 89% of the match play value is obtained. That's correct. Ignoring pushes, a .79 EV implies a 90% chance of winning the hand and 10% chance of losing it. 90% x 1 + 10% x (-1) = .80 ~ .79. However, with the match, 90% x 2 + 10 % x (-1) = 1.70 ~ 1.68. 1.68 - .79 = .89, so 89% of the match play value is received.

---------------------CALCULATION PROCEDURE---------------------
To determine my match play strategy, I did the following:

1) I pulled the wizard's data on the basic strategy EV of every option per his Blackjack Appendix 9 — 6 Decks, Dealer Hits Soft 17 (https://wizardofodds.com/games/blackjack/appendix/9/6dh17r4/). Note: The game I play has RSA, but the wizard provides no RSA option for the data. This is not relevant, as you always split aces whether RSA is available or not.

2) I used the EV to reverse engineer the probability of a win using the formula p(w) = (EV + 1)/2, and the probability of a loss being the balance, p(l) = 1 - p(w). This has a significant flaw in that it ignores pushes. The player retains his match play after a push, so a push is valuable to losing in that the match play can be played on a second hand. However, as only approximately 8.5% of hands push (https://wizardofodds.com/gambling/promotional-chips/) this error is unlikely to have much impact on match play strategy. I did make sure to adjust for doubling down by dividing the EV by 2 before calculating the win percent.

3) I then re-multiplied the percent win and loss by the new payouts (win pays 2, loss loses 1, double win pays 3, double loss loses 2). For purposes of this exercise, I assumed that splitting was equivalent to doubling in terms of payouts, although it most certainly is not. Net pushes are common, while if the winner is the matched hand the push is really a win.

4) I found the decision with the highest match play EV for each composition dependent strategy, and found the (simple, not weighted) average of the decisions. In no case did the average actually appear necessary (for instance I assigned standing a value of 1, hitting a value of 2, doubling a 3, and splitting a 4). No hands ended up with a 1.95 or 2.05 or whatever, so my conversion to total dependent strategy, while inaccurate in theory seems to have no practical error.

5) I charted the results and compared with the appropriate basic strategy chart, noting the 10 differences listed above.


---------------------FINAL NOTES---------------------
Sadly, this looks to have been a purely academic exercise. The increases in EV are just not dramatic enough to even warrant memorizing the strategy. It's probably just best to play the match play with basic strategy and spend time learning indexes, new counting methods, or other AP techniques. Although I do plan to split 9's against an A when I have a match going. Just because I can.

There's a reason why you split more often when using match-play: In essence you are able (or rather forced to) "split for less" which makes some of the high-upcard splits correct. You didn't mention it, but from some calculations I recall the Wizard doing you would NOT split 4's at all with match-play because most of the advantage there comes from DAS potential; when you aren't allowed to double for the full amount that stifles the benefit there.

Here's an interesting note: Besides you getting a substantial boost on the game edge, if you could split for just a minuscule percentage of your original bet (or nothing), you would split all pairs except for 4's (except when regular BS in DAS games calls for splitting), 5's, 9's vs. 7, and 10's (in other words the only pairs you wouldn't split are those whose starting position would be weakened by splitting). You would split for the full amount on all +EV hands that call for splitting, and split for as little as possible on the -EV ones.

Quote: kmcd

...
11 v A: Hit (for a .01 increase in EV)

Soft 13 v 5: Hit (.03)
Soft 15 v 4: Hit (.01)
Soft 18 v 2: Stand (.02)
Soft 19 v 6: Stand (.10)

2,2 v 8: Split (.01)
3,3 v 8: Split (.04)
6,6 v 7: Split (.01)
7,7 v 8: Split (.08)
9,9 v A: Split (.03)

...

My infinite-deck analysis agrees with your deviations quite closely. But it would hit soft 13 vs 6, and it would hit 6,6 v 7.

However, with a $10 match coupon and $10 cash, for example, it would split 6,6 v 7 if it could double-down for $20 afterwards on the coupon hand. How strict are your cardrooms' dealers on the use of match coupons? That is, would some dealers give you the option of doubling for $20 in that case? Also, will some dealers let you split by putting up either $10 or $20?

When you split or double-down with the match play, do you match the entire amount or just your cash bet? I feel kind of silly asking, since I've used plenty of match plays in my day, but to be honest I don't think I've ever been presented with one of these hands while using a match play.

Quote: AcesAndEights

When you split or double-down with the match play, do you match the entire amount or just your cash bet? I feel kind of silly asking, since I've used plenty of match plays in my day, but to be honest I don't think I've ever been presented with one of these hands while using a match play.

I've done both..
$5 with $5 Matchplay : $10 split/double
$5 with $5 Matchplay : $5+$5matchplay split/double (mirroring my original bet, in essense)

I know Grosjean had an article about all kinds of promo chips http://www.beyondcounting.com/pdfs/beyondcouponsbjfo.pdf
You might give it a look.