The wizard is wrong on the probility of pushing giving the first card is an ace!

What the wizard says about the Free Ace

The free ace coupon may be used as an ace, in lieu of the first card dealt, in blackjack. According to my blackjack appendix 14, the expected value of an ace as the first card is 50.4% of the amount bet, assuming liberal six-deck rules (dealer stands on soft 17, double after split allowed, re-splitting aces allowed). These statistics are on a per hand basis, and include pushes. The probability of a push in blackjack is 8.5%. I have not calculated the conditional probability of a tie, given the first player card is an ace. Assuming the push probability is still 8.5%, and the player keeps the coupon on a push, the value of a free ace is 55.1% of face value, under the same liberal rule assumptions.

The 8.5% chance of a push is before any cards have been dealt and the cards are random it is not assuming the first card that you got was an ace. Having a first card is an ace increases your chances of finishing the hand with a 17-21 so it increases the odds of pushing because these are the only hands that can push. A 12-16 can't push and a 22-26 can't push. I would be willing to bet a $100 that the probality of pushing with first card is an ace is higher than 8.5% given that you follow basic strategy.

I'm also assuming that the player refuses to take even money if they get a blackjack and the dealer has an ace up. Taking even money is normally the wrong play and if you take it in this situation you will automatically lose your ace. Pushing on a blackjack is not that bad.

Quote: cardcounter

What the wizard says about the Free Ace

The free ace coupon may be used as an ace, in lieu of the first card dealt, in blackjack. According to my blackjack appendix 14, the expected value of an ace as the first card is 50.4% of the amount bet, assuming liberal six-deck rules (dealer stands on soft 17, double after split allowed, re-splitting aces allowed). These statistics are on a per hand basis, and include pushes. The probability of a push in blackjack is 8.5%. I have not calculated the conditional probability of a tie, given the first player card is an ace. Assuming the push probability is still 8.5%, and the player keeps the coupon on a push, the value of a free ace is 55.1% of face value, under the same liberal rule assumptions.

The 8.5% chance of a push is before any cards have been dealt and the cards are random it is not assuming the first card that you got was an ace. Having a first card is an ace increases your chances of finishing the hand with a 17-21 so it increases the odds of pushing because these are the only hands that can push. A 12-16 can't push and a 22-26 can't push. I would be willing to bet a $100 that the probality of pushing with first card is an ace is higher than 8.5% given that you follow basic strategy.

It seems a little odd that you're saying that the wizard is wrong about a calculation that he explicitly says he hasn't done...

First, I think it is rather rude to come into my site, guns blazing, trying to embarrass me over an error. I would prefer to be contacted by Email or Private Message if you think I've made a mistake about something.

Second, this comes down to simply whether or not the player gets to keep the free ace after a push. As far as I know, he doesn't, and you feel he does. Maybe I'm in error about that. I haven't seen a free ace coupon in years, so I can't easily run out and ask a dealer about it.

Quote: Wizard

First, I think it is rather rude to come into my site, guns blazing, trying to embarrass me over an error. I would prefer to be contacted by Email or Private Message if you think I've made a mistake about something.

Second, this comes down to simply whether or not the player gets to keep the free ace after a push. As far as I know, he doesn't, and you feel he does. Maybe I'm in error about that. I haven't seen a free ace coupon in years, so I can't easily run out and ask a dealer about it.

To the wizard sorry if I embarrassed you on your site. But I would be willing to take a bet that pushing happens more than 8.5% when first card is an ace using proper strategy. The simple fact of being able to take your first hit free of busting allows you to get more hands of 17-21.
I have seen the ace coupon go both ways some leave it on a push and some take it. If they try to take it I ask why are you taking it and sometimes it will work and they will leave it. Some dealers will treat it like a match play coupon and leave it on a tie.

Quote: Wizard

I would prefer to be contacted by Email or Private Message if you think I've made a mistake about something.

Actually, I didn't know you felt that way.

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Quote: odiousgambit

Actually, I didn't know you felt that way.

It depends on the context. If the OP had been more diplomatic about questioning the assumptions underlying my analysis that would be fine. However, it is another matter to start the discussion with a declaration that I'm wrong. There is something to be said for tact and respect.

Quote: Ibeatyouraces

according to beyond counting, a free ace coupon is actually worth less than a normally dealt ace.

Is that because of the effect of removal? A real ace removed means more tens left in the shoe, thus a greater chance of a blackjack.

Is the coupon splittable? I would think the ability to split AA might significantly add to the value of the natural ace.

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Extra Extra read all about it: CardCounter is wrong on the spelling of probility (probability).

Quote: rdw4potus

Is the coupon splittable? I would think the ability to split AA might significantly add to the value of the natural ace.

Yes if you land another ace which are only 1 in 13 odds with the coupon instead of the usual 220 to 1 odds of getting two aces.