Spanish 21 EV?

[Gronbog]

In the case of craps, it is likely that a slight increase in variance for the pass line bet tips the balance slightly in its favour. As I said, too much math to do on a tablet. Maybe someone else will take a crack at it.

[Three]

Just played Spanish 21 with match plays, and surrendered twice (I had 6 match plays), both of which I wouldn't have done previously (since the EV for the play was better than -0.5, but worse than -0.333). Thanks to everyone who contributed toward lowering my house edge at SP21! Agreed that you can't use coupons in most cases, but in places where you can, this is awesome information. :-)

You should also not double as much. You are tripling your money at risk for only double the payoff. I question whether you should double any hand you would rescue when this is the case. Certainly you would never double a 3 card hand that you would rescue. If you don't double and would have rescued you are now drawing for 3 times the money at risk for a 5 card 21 and 4 times the money at risk if you draw twice (or don't double a 4 card total) after the rescue would have occurred. Things get a lot more complicated than you are likely taking into account.

[All Clear]

You should also not double as much. You are tripling your money at risk for only double the payoff.

Your math is off- there is no tripling. Instead of "doubling" down, you can "133%" down, putting four green chips instead of what might otherwise be three.....

You should not double as much? Nope. You should double MORE often, unless I figured this out all wrong. Consider a typical bet with a $25 chip on top of a $25 match-play coupon in Spanish 21- an (aprox) $37.50 total bet (turns into $75 if it wins, or zero if it loses). Now imagine, instead of doubling for $37.50 in chips, you can double for $50 in chips? Obviously, you can, in any casino. In essence, you are allowed to "double for more".

Then, when surrendering after doubling (rescuing, also called "forfeiting") in Spanish 21, you get back your doubled amount, and lose the regular bet. This means if you double down for less, rescuing is bad- since you only get back the "for less" part, and the casino is taking a full bet. But in our case, a rescue means you get back $50, and the casino keeps only $37.50 (aprox). This is why you would rescue more in Spanish 21- though the numbers show the only change is when you have a stiff total against a dealer 7, in which you should now surrender.

[Gronbog]

All Clear is correct. Check Grosjean's chart on page 11. If you can double for the full amount with live money, then you will double more frequently for blackjack. A similar principle will apply to Spanish 21, but perhaps not as much, due to the possibility of multi-card bonus hands.

[ZenMaster_Flash]

In the case of craps, it is likely that a slight increase in
variance for the pass line bet tips the balance slightly
in its favor. Maybe someone else will take a crack at it."

The above is seemingly incorrect, or at least
I think that that is the case. Will someone who
understands this issue please help me out here.
This Sunday I will have $500 in Match Play to use,
and I will gladly use them in (20) $25 denominations.

[Three]

Sorry. I confused splitting with doubling. I was tired and haven't been using MP at BJ in a long time. I usually exchange it for free slot play at 1:1. Yes when you rescue you lose your original bet only. The rescue rule should increase the amount you double when you would rescue, but the multicard bonuses will have some effect in the other direction when you have more than 2 cards.

If you use a matchplay at a game you are going to play anyway to replace one of the chips you would have bet, the matchplay only has value if you lose. If you add it to your chips you would otherwise bet it only has value if you win. If you take away half the face value of the matchplay from the bet you would make anyway it is always worth half the value of the coupon no matter which way the bet is decided, unless you get a bonus payout. You should always make sure they pay all the bonus payouts for a matchplay before deciding to use it on a game. Almost all the places that give me matchplay coupons won't pay more than 1:1 on the coupon. This casino is the one exception in the set of places that give me matchplay and won't let me exchange them for free slot play.

As for the Pass Line/Don't Pass debate for matchplay. The Don't Pass is better if the coupon is saved on a tie but the Pass Line is better if the coupon is lost on a tie. There is no tie for the Pass Line but the Don't Pass pushes on a come-out 12 so, in that situation, the coupon would be lost if bet on the Don't Pass.

[Joe Mama]

Sorry. I usually exchange it for free slot play at 1:1.

Excellent choice trading EV of ~50% on even money bet for 98+%.

[Gronbog]

The above is seemingly incorrect, or at least
I think that that is the case. Will someone who
understands this issue please help me out here.
This Sunday I will have $500 in Match Play to use,
and I will gladly use them in (20) $25 denominations.

I fully understand he issue. As I tried to demonstrate using the extreme examples of roulette and coin toss, the bet with the highest EV is not always the best choice for a match play. The best choice is determined by the interaction of the EV and variance with the latter being the more dominant factor. A bet which loses more often than another will often be the better choice.

In the case of craps, the pass line bet has slightly lower EV than the don't pass. Since they each pay 1:1, this can only be because the pass line loses slightly more often than the don't pass. This would be the factor which makes it the better choice for match play.

If you have a stack of match plays to use, I suggest consulting Grosjean's list and choosing the highest performing bet that they will allow you to make.

[Three]

I bolded the following at the end of my relatively short post so it would be read. I guess I should have just made a second post.

As for the Pass Line/Don't Pass debate for matchplay. The Don't Pass is better if the coupon is saved on a tie but the Pass Line is better if the coupon is lost on a tie. There is no tie for the Pass Line but the Don't Pass pushes on a come-out 12 so, in that situation, the coupon would be lost if bet on the Don't Pass.

[Joe Mama]

I fully understand he issue. As I tried to demonstrate using the extreme examples of roulette and coin toss, the bet with the highest EV is not always the best choice for a match play. The best choice is determined by the interaction of the EV and variance with the latter being the more dominant factor. A bet which loses more often than another will often be the better choice.

In the case of craps, the pass line bet has slightly lower EV than the don't pass. Since they each pay 1:1, this can only be because the pass line loses slightly more often than the don't pass. This would be the factor which makes it the better choice for match play.

If you have a stack of match plays to use, I suggest consulting Grosjean's list and choosing the highest performing bet that they will allow you to make.

Example match play coupon:

*even money bet $10 coupon, EV =50% of $10 + 50% of $0 = $5
*2 to 1 bet $10 coupon, EV = 33% of $20 + 33% of $0 + 33% of $0 = $6.67

* 9 to 1 bet. EV =10% of $90 + 90% of $0 = $9
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[Gronbog]

I promised to address the outstanding issue of the correct model for determining the proper surrender strategy in the presence of a match play coupon when I returned home. I now have the data I need to do that. The full post will follow this one shortly and it will be quite lengthy. For those interested only in the bottom line, here is an executive summary of what I will be posting:

• The OP's model for determining the match play surrender strategy is incorrect
• The correct model is Grosjean's loss rebate model
• I have reproduced Grojean's strategy deviations and coupon value for blackjack (MPR 20/20 BJ 3/2 DOA DAS SP3 LS) using my software
• http://gronbog.org/results/blackjack...-20-BJ3-2.html
• See the tables on page 11 and 16 of Grosjean's article for comparison
• I am generating the correct strategy for the OPs Spanish 21 game and will post it when the sim converges

[Gronbog]

There is an unresolved issue in this thread that I am able to address, now that I am back home and have access to my computers and software. The OP asked for a S17 Spanish 21 strategy chart with the EVs of each action included. He wanted this because he found a place which would allow him to surrender his match play bet on Spanish 21 with the implementation being that he would keep his money and they would take the coupon. His intention was to use the strategy chart to decide when to surrender his match play. The strategy he intended to use was to surrender any hand for which the EV was -1/3 or less.

The reasoning was that, by giving up the coupon, which is worth approximately 50% of the matched value, he was giving up 1/3 of his total bet of 1 unit live money and 0.5 units for the coupon. My response was that he was actually breaking even because he kept his money and only relinquished the coupon.

And so here we are.

The OP's model

It is often difficult to refute an incorrect mathematical model, especially when the logic behind it seems compelling. I am reminded about how hard it is to convince progression players that their systems will not work in the long run. In this case, if you use the word "value" loosely, the OPs logic is attractive. The problem is that the correct term to use is that the coupon has an "expected value". By using it, you can expect a certain positive result once the coupon is resolved. Note that I didn't say "lost", because this expected value is only realized once the process is completed and the coupon is always taken away at that point. I think that Grosjean was being deliberately careful when he used the word relinquished in his article.

Having said that, here are a few problems with the OP's model. He believes that relinquishing the coupon when surrendering, he is losing 1/3 of his total bet. However:

• When we win, we are paid 2 units and the coupon is relinquished, but do we then say that the value of winning the bet is only 1.5 units?
• Similarly, when we lose, have we lost 1.5 units?
• What about the "value" of the coupon itself? As Grosjean showed, the "value" of the coupon depends on which game you are allowed to use it on and what strategy you intend to play. Why then is 50% the correct value of the coupon here?
• What about live chips? If we are a basic strategy player and we lose a $100 chip, do we say that we only lost $99.50 because the "value" of the chip is only that much due to the 0.5% house edge? Does a card counter say he lost $102 because his overall edge is 2%?
• Even if it was correct to deduct the "value" of the coupon from the final outcome, the OP would be comparing against the wrong EVs for the various other actions. This is because the EVs of every action change in the presence of the coupon (they are all higher).

All of these issues are due to the improper application of an arbitrary expected value of the coupon to the very calculations which determine that value. That's a mathematical paradox which is one very good reason why that model cannot be correct.

Grosjean's Model

The correct way to model the coupon is as a loss rebate. Grosjean explained the concept very simply and very well and then went on to list the "value" of the coupon for various games, conditions and strategies using this model. It is a bit ironic that the OP seems to accept ~50% value (for blackjack) obtained from Grosjean's loss rebate model but then decided to use a different model to devise his strategy.

Grosjean does not show his calculations, but I (earlier in this thread) showed how the value of 0.868 (or $8.68 for a $10 coupon) for American roulette is calculated using the loss rebate model. Here it is again for reference:

(1/38)x35x2 + (37/38)x(-1x2 - 1) = (70/38) - (37/38) = 33/38 = 0.868

There are a few things to realize about this:

• The model performs all calculations as usual based on a 2 unit bet (1 unit live, 1 unit for the coupon), except that ...
• Losses are rebated by the face value of the coupon (1 unit)
• There is no rebate for a win
• There is no rebate for a push (but additional value is generated if the coupon is retained)
• The final value of the coupon is expressed in units of the face value of the coupon

Based on the above you can see that the value of the coupon is generated from that fact that the loss rebate changes the payout structure of the game. At no time is the perceived "value" of the coupon subtracted from the EV of an outcome. It is simply that, when we lose, we lose less than normal.

Here is another important observation. The "value" of the coupon is the amount of additional live money you can expect to have in your pocket after the process of using the coupon has been resolved. In the case of roulette, each time you bet your coupon along with $10 live money, you can expect to have an additional $8.68 in your pocket, on average, after the bet is resolved. This will come into play when we discuss surrender in blackjack below.

In the case of blackjack, for a SP3 game with DAS, with a 2 unit bet and assuming that doubles and splits are made with live money, losses can range from 2 units to 16 units. In order to calculate the value of the coupon, each of these categories of losses is reduced by one unit and the EV is then calculated normally. Furthermore, as the cards are dealt and as each decision is presented to you, the value of the coupon changes based on the new expected distribution of results for each action. The "value" of the coupon is simply the new house edge calculated using the modified payout structure and the resulting modified basic strategy.

Now we can finally address the issue of surrender for the implementation of relinquishing the coupon and keeping your live money. In the loss rebate model, there is no loss and therefore no rebate. The coupon is relinquished as part of the resolution of the hand and is not "lost". If you had decided to take some other action, the coupon would have some (positive or negative) value for that particular hand based on the expected distribution of various levels of wins and losses for that action. However, the decision to surrender reduces the value of the coupon to zero since that is now the only possible outcome. You end up with the same amount of live money that you started with. The EV of surrender in this situation is zero.

The correct surrender strategy is therefore to surrender any hand for which the EV is zero or less under the modifed payout structure and strategy.

Confirmation

I implemented the loss rebate model in my software years ago when I first read Grosjean's article. I was able to then reproduce his suggested basic strategy changes for the game which is common in my area. Since returning home, I have modified and used my software to also reproduce his suggested surrenders for the same game.

http://gronbog.org/results/blackjack...-20-BJ3-2.html

Some notes:

• The game is S17 DOA DAS SP3 BJ 3/2 LS
• The model assumes that, when surrendering, the coupon is relinquished and that the live money is kept (EV=0)
• The model assumes that all doubles and splits are made using live money.
• The hand with the coupon is played according to the modified strategy, even after splitting.
• Split hands with only live money are played according to the normal basic strategy.
• Hover your mouse over any cell in the table to see the EVs of each action under the modified payout structure.

Compare my chart with Grojean's table on page 11 for the "MPR [20/20]: Relinquished after one round" game and table LSII (page 16) for the same game. You will see that the strategies are the same. You will also see that my player edge (51.4477% = 0.51447) agrees with his value of $5.14 for a $10 coupon (table LSII).

With some confidence that my software model is correct, I am currently generating the proper strategy for S17 Spanish 21. I will post that strategy once the simulation has converged. This will be the strategy that the OP should use for playing his match play coupons.

[All Clear]

I nominate Gronbog for "most helpful poster of the year". This will only assist people in Spanish 21 (or blackjack) who, if they surrender, only lose their match play, but not their main bet.... but he/she still did so much work toward finding the correct answer.

I have reproduced Grojean's strategy deviations and coupon value for blackjack (MPR 20/20 BJ 3/2 DOA DAS SP3 LS) using my software

http://gronbog.org/results/blackjack...-20-BJ3-2.html

See the tables on page 11 and 16 of Grosjean's article for comparison

Excellent work.

In this case, if you use the word "value" loosely, the OPs logic is attractive.

The OP is a really good-looking guy, so both he, and his logic, are attractive. But back to match-play coupons- the easiest way to value an item, is what you would pay, in cash, for it. If you would pay somewhere between $4.50 and $5.50 for a $10 match-play coupon, valuing the coupon at 50% (aprox) of it's listed dollar amount, seems like the right way to go.


My responses below are embedded for each bullet, with the first word I write in caps, so one can see where I start chatting.

Having said that, here are a few problems with the OP's model. He believes that relinquishing the coupon when surrendering, he is losing 1/3 of his total bet. However:

• When we win, we are paid 2 units and the coupon is relinquished, but do we then say that the value of winning the bet is only 1.5 units? YES. Absolutely. When I bet a match play, with a regular bet, I am betting 1.5 units, so when I win, I win 1.5 units.
• Similarly, when we lose, have we lost 1.5 units? YES. Absolutely. When I bet a match play, with a regular bet, I am betting 1.5 units, so when I lose, I lose 1.5 units.
• What about the "value" of the coupon itself? As Grosjean showed, the "value" of the coupon depends on which game you are allowed to use it on and what strategy you intend to play. Why then is 50% the correct value of the coupon here? BECAUSE this assumes we are using it at Spanish 21 (or Blackjack). If I am allowed to use the coupon on a single number in Roulette, yes, it is worth much more. But as per an earlier reply on this thread, every single casino of the eight in my general area, restrict where it an be used, to "even money" type bets.
• What about live chips? If we are a basic strategy player and we lose a $100 chip, do we say that we only lost $99.50 because the "value" of the chip is only that much due to the 0.5% house edge? Does a card counter say he lost $102 because his overall edge is 2%? WHILE I understand your point, it is irrelevant- I am approximating the value of the match-play coupon at 50% of the base bet, even if it might actually be 49%, or 51%. There won't be a major difference in strategy, and likely won't even be a minor difference in strategy, whether the match-play coupon should be valued slightly different than 50%.
• Even if it was correct to deduct the "value" of the coupon from the final outcome, the OP would be comparing against the wrong EVs for the various other actions. This is because the EVs of every action change in the presence of the coupon (they are all higher). THIS is a true statement, and while I didn't type anything saying this, it is something I considered. After all, if one knows how to properly use a match-play coupon (as we will, hopefully, once your simulation is done- thanks again for that!), the value of it is slightly higher, and we might want to be more likely to save our match-play coupon than a typical ploppy, who doesn't know the right way to use it.... but this makes the calculations so much more complicated, that I passed it over. If you can incorporate all the changed EV actions with the presence of the coupon, awesome! Extra Credit will be awarded. :-)

With that being said, Grosjean's model works fine, is superior to my approximations, and I fully agree that the best way to work out this problem is, as you wrote, using the "value" of the coupon as the amount of additional live money you can expect to have in your pocket after the process of using the coupon has been resolved. While I would expect that my surrender strategy (and my forfeit strategy, and the double-down strategy that I generated, but haven't posted in this thread) would be very VERY close to what your simulation shows, I look forward to your results. Thanks! :-)