Spanish 21 EV?

[Gronbog]

If we agree on this ...

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

then you cannot believe these ...

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.

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.

They are contradictory.
Once it has been bet, the coupon no more than a reminder to the dealer that the payout structure of the game has been changed.

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.

I think that you're in for a bit of a rude surprise. I tried applying your surrender model to blackjack and got nothing close to the strategy that Grosjean and I have both independently computed.

Thanks! :-)

My pleasure.

[All Clear]

I now have a match play strategy for S17 Spanish 21 but, while reviewing it, I realized that the implementation used for rescuing (surrendering) a double is the same as the one for normal surrender. i.e. keep only your original live money and relinquish the coupon. So the loss is 2 units plus relinquishing the coupon. This is probably not the right implementation since, in Spanish 21, when you rescue a double you keep the doubled amount and lose the previously bet amount.

The correct implementation, and the one more likely to apply in a real game would be to keep the doubled amount (as usual), lose the original bet (2 units) and be rebated by the value of the coupon (1 unit) for a loss of only 1 unit.

The strategy I generated assumes that when rescuing on a double down (when using a match-play), instead of losing half your total bet, you lose 3/7 of your total bet, since (if betting $25 with a $25 match play) you would rescue (and keep) $50, while only losing to the casino $25 and a $25 match play (which, at 50% of face value, would be $12.50). My rescue strategy (generated with these assumptions, using EV tables) is identical to SP21 basic strategy, other than rescuing on an 11-16, with a dealer 7, which we should now rescue (but do not rescue if no match-play is involved with the bet).

While I did not generate exceptions for multiple cards, the only two card doubles that are changed by the ability to double down for more, are soft 15 v 6, and soft 16 v 5. Without a match play, both are (barely) hit situations, but with the ability to double down for $50, when only betting an original $25 and a $25 match-play (in essence, doubling down for more, since the original bet is valued at $37.50, aprox), they both move to the "double" category.

This works if we value a match-play at 50% of the amount you get if you win. This all gets more complicated, if a match-play is not valued at 50% of it's face value, which brings me to attempting to prove that point.....

If we agree on this "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"

then you cannot believe this "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."

They are contradictory.
Once it has been bet, the coupon no more than a reminder to the dealer that the payout structure of the game has been changed.

False. Once it has been bet, the coupon is still worth $12.50 (again, I am using a $25 base-bet unit), or a number within a few cents of that. That is why if you win, you have a total of $75 in front of you. You win 1.5 units, and are going from the original 1.5 units of $37.50 (a green chip and a coupon) to three green chips, totaling $75. It is also why if you lose, you now have nothing from your bet- you lost 1.5 units. This jives well with the first statement- how the match-play coupon is worth the average amount you'll have in your pocket afterward, due to playing it. If you win half the time, and lose half the time, you'll have $25 extra half the time, and $0 half the time, for an average gain of the same $12.50. :-) I am aware that you don't win 50% of hands, but even if it is 44%, the approximation is acceptable for match-play problems, I figure. Note that in Grosjean's article, he approximates the value for the match-play in blackjack as a number relatively close to 50% of the base bet, as well.

It could be I'm not explaining it well- I'm a math guy (I used to be a certified actuary, and now work as an engineer), and people have told me that I use numerical explanations that are not clear to all. In any case, you wrote that I am "in for a bit of a rude surprise", which I look forward to getting. If it makes me a better SP21 player, I'll take all the rude awakenings I can get. Thanks, Gronbog. :-)

[Gronbog]

The strategy I generated assumes that when rescuing on a double down (when using a match-play), instead of losing half your total bet, you lose 3/7 of your total bet, since (if betting $25 with a $25 match play) you would rescue (and keep) $50, while only losing to the casino $25 and a $25 match play (which, at 50% of face value, would be $12.50).

At least we can agree on the mechanical implementation of resucing a double with the coupon. I still disagree with your mathematical model of placing a fixed and (somewhat) arbitrary "value" on the coupon for the purpose of calculating it's actual value when surrendering or rescuing.

False. Once it has been bet, the coupon is still worth $12.50 (again, I am using a $25 base-bet unit), or a number within a few cents of that. That is why if you win, you have a total of $75 in front of you. You win 1.5 units, and are going from the original 1.5 units of $37.50 (a green chip and a coupon) to three green chips, totaling $75.

I showed above how the value of the coupon changes as the cards are dealt and each decision is presented. This contradicts your assumption that the coupon has a fixed value throughout and is one reason why applying your method to blackjack does not match the results that Grosjean and I have independently computed using different algorithms (CA and simulation respectively.)

This jives well with the first statement- how the match-play coupon is worth the average amount you'll have in your pocket afterward, due to playing it.

No. You missed a key word. I said "additional money". You started with $25 live money and when you win you now have $75 which is $50 more or 2 units. Similarly when you lose you go from $25 in live money to zero, which is -$25 in additional money or -1 units.

the approximation is acceptable for match-play problems, I figure.

This is one area in which most arguments fail for incorrect mathematical arguments. The introduction of an "acceptable" approximation. You really think that a 6% difference in win rate represents an acceptable approximation when computing basic strategy?

Note that in Grosjean's article, he approximates the value for the match-play in blackjack as a number relatively close to 50% of the base bet, as well.

Actually, I see no approximations at all in his article. Some of the results can be duplicated by calculation, as I showed with roulette and craps. Others (like blackjack) require CA software which also produces exact results. My own results are approximate only because I use simulation. Also, the value of the coupon for the blackjack games he examined ranges from 0.430 to 0.519, which is why I describe your use of 0.5 as arbitrary. We actually don't know the value of the coupon for S17 Spanish 21 using basic strategy.