Spanish 21 EV?

[Gronbog]

How can the EV of surrender be 0? Either it is -.5 or -.33 but under no scenario is surrendering breaking even

You have a match play coupon for $100. You also have a $100 chip. You bet the coupon along with the $100 chip. After your first two cards are dealt, you decide to surrender. They take your coupon and you keep your chip. You have broken even. You bet the coupon and the chip and got zero back for your bet. This is a MPR coupon which you would lose regardless of the outcome of the hand.

FWIW, I'm running a sim using this model as we speak in order to generate the adjusted basic strategy for S17 DAS and it is converging on the same strategy variations that Grosjean published in his article, including for surrender.

[Gronbog]

Gronbog- I received your sheet. Thanks so much! I'll analyze it, and if anyone wants the info, shoot me a note on this page starting on November 7th or so (I need time to examine each cell, and am not a full time AP).

Thanks, but depending on how this debate is resolved, it may or not end up being of any use to you.

[All Clear]

I examined some hand situations that Assume_R sent me six and a half years ago (see "https://www.blackjackinfo.com/community/threads/spanish-21-expected-return-charts.22380/") and examined the EV for some that coincide, such as 15 v T, 17 v A, etc. The expected values for each hand that you sent me were within 1 percentage point of his sheet each time, and I wouldn't have expected them to be the same (your simulation is 2 billion rounds, which while a lot, is not enough to get an exact figure- I think his results were with simulation as well. Plus, you break them down by hand type, and he breaks it down by count....). Moreover, the results for cases where we would otherwise stand (such as 15v2, 15v3, etc.) match what I find in Katarina Walker's book. In summary, the results in your spreadsheet look quite reasonable.

The results to my original question seem quite easy to find now- when playing S17 Spanish 21 with a match play, and if surrendering would cause you to only lose your match play, just surrender whenever the best EV decision is still worse than -0.333. I believe that includes the following cases, and (without counting) includes ONLY the following cases:

13vT, 13vA, 14v9, 14vT, 14vA, 15v2, 15v8, 15v9, 15vT, 15vA, 16v2, 16v7, 16v8, 16v9, 16vT, 16vA, 17v8, 17v9, 17vT, 17vA (obviously, as it is a surrender for basic strategy also).

Notice the oddity that in S17 Spanish 21 when only losing 33.3% on a surrender, one should surrender 15v2, but not 15v7- which isn't as bad hand as I thought. in fact, 15v7 is even preferable (higher EV) to 15v3 (though neither is a surrender). A few of the figures in Gronbog's sheet seemed odd, until I thought more about it.

Notice how only one hand in Spanish 21 has worse than a -0.5 EV (17vA), but exactly 20 hands, the worst starting 20 hands in the game, are worse than -0.333 EV.

[All Clear]

One further note regarding pair splitting: surrender 7,7vT and 7,7vA, but NOT 7,7v9. I know we surrender all other 14's against a 9, but the 3:2 bonus if we get another 7, when hitting 7,7, is enough to move the EV higher than -0.333 for this matchup. With 8,8, the results are the same (for different reasons, obviously)- surrender 8,8vT and 8,8vA, but not any other 8,8 matchups.

[Meistro123]

You have a match play coupon for $100. You also have a $100 chip. You bet the coupon along with the $100 chip. After your first two cards are dealt, you decide to surrender. They take your coupon and you keep your chip. You have broken even.

No, you have not broken even, you have lost precisely one match play coupon, the value of which we can estimate at $50.

[Gronbog]

I'll think about this some more, but not too much. I'm on vacation and at the airport waiting for my flight. I'll be back on the 12th. I have some ideas about why we have our wires crossed on this, but I need some time to formulate these thoughts.

In the mean time, the OP seems happy with the data I sent him.

[Three]

No, you have not broken even, you have lost precisely one match play coupon, the value of which we can estimate at $50.

No. Once the matchplay was bet and has a matchup its value depended on the matchup. The decision to surrender maximized that value of the matchplay at that point. That is because your EV was highest by surrendering the matchplay and losing no money. If you would not have properly surrendered the matchplay your EV would have been less so the matchplay was worth the most by surrendering it. That is called maximizing the value of the matchplay. Like having the matchplay may cause you not to split hands you would split otherwise, like 3,3v2 in BJ. That is because it changes the added value of the matchplay to be less when making some defensive splits.


If you get a 8,7vA in 6 deck H17 BJ is -0.503074 is the EV of the hand for the best decision, hitting. To make the math easier we will call it an EV of -0.5 and negate pushes to illustrate what the value of the coupon is once the hand is dealt. That means you win one time and lose three times for a cycle of 4. If you won the $100 MP coupon 1 time out of every 4 it is worth $25, which is half the value of $50 you are putting on it. If you decided to stand with an approximate EV of -0.6 (again slightly rounded to make math easy) for no coupon bet the value of the coupon would be less. If you win 1 time for every 4 times you lose for a cycle of 5, the EV is -0.6 so the match play coupon would be worth $20. If you could decide to take the matchplay back after you bet it and see your matchup with on penalty then you could restore its value to the original $50. But the casino won't let you do that.

The way you decide to play a matchplay is the decision that gives you the highest EV including the matchplay's resolution. That has nothing to do with the value of the matchplay at any point. Surrendering and losing only the match play has an EV of 0. ) EV means when the matchplay was resolved you lost no money. You just lost a piece of paper that you can't cash but used it to its best value given the situation. You didn't lose half the face value of the matchplay. You won half the value of the matchplay because if you surrendered while just losing the matchplay and keeping all your chips, rather you would have lost half the value of the matchplay in chips as compared to losing no chips. So the value of the coupon when surrendered with these rules for surrendering it was in fact half its face value. But you saved the difference in chips compared to the next most desirable decision.

[All Clear]

I started thinking about the more complicated adjustments to make when betting a matchplay in Spanish 21, and here is the next step (I already, in my last two posts, pointed out proper hitting/standing/surrender decisions, including for when you have pairs). I now starting thinking about the forfeit (after doubling) option. By definition, when we double down, it is because that is positive EV, so we want to get as much money out as possible. This means when given the option to double down when betting (at S17 SP21), say, $50 in chips and $50 in match play, we would double for the maximum amount ($100 in chips, and not $50 in chips and another $50 match play, which only has an EV of $75 total). In effect, we are "doubling down for more". :-)

When forfeiting after doubling, the dealer takes the original bet, and gives you back the amount used to double. This means, if you forfeit when wagering the amounts I show, you are getting back $100, and accepting a loss of just $75. It should be obvious to all that we should forfeit more often, therefore, when using a matchplay. Getting back 4/7 of your bet, or $100 out of $175, means we should surrender after doubling whenever our EV is less than -.429, as opposed to a regular double, when we forfeit whenever our EV is less than -.500. Please feel free to check my math, if you like (or comment if you disagree).

This leads to the following forfeit basic strategy:

12-16 v 7,8,9,T,A
17 v A

This is identical to regular forfeit strategy, other than a stiff hand vs a 7, which is a forfeit when using a match play, but a stand when using regular chips for the entire bet. If I knew this at the start, I probably wouldn't have crunched all these numbers for this small adjustment, but I guess it takes one person to do the work, to figure it out for everyone, to make sure there aren't other changes to make in strategy.

[All Clear]

Since there seem to be no further replies, it doesn't seem to make sense to post additional adjustments to make, when using a match-play, in Spanish 21. If I am incorrect, please send me a pm, or post below, and I'll be happy to post when to double-down (it is done more often) in the game, which I finished figuring out today (it was a busy day- the NYC Marathon in the rain really drained my first 2/3 of my Sunday).

To those reading this thread, much of the back-and-forth above can likely be skipped, if you agree that a match play, when played on a table game like Blackjack or Spanish 21, has an EV of just about 50% of what you would win, if you win. There is a dispute about this above.

[Gronbog]

I have some more points to make, and evidence to present , but am not planning on doing so until I return from vacation and have access to my computers. That will be sometime next week.

[refinery]

I have some more points to make, and evidence to present , but am not planning on doing so until I return from vacation and have access to my computers. That will be sometime next week.

You're doing an awful lot of talking about vacationing without actually vacationing!

[ZenMaster_Flash]

Readers of this thread are reminded that almost no casino in North
America will permit the use of Match Play on Spanish21 games.

[Gronbog]

You're doing an awful lot of talking about vacationing without actually vacationing!

Haha, you're probably right. But posting from poolside while enjoying a tequila sunrise beats my normal day job!