Last Updated: January 17, 2019

# Value of a Free Ace

## Introduction

Sometimes a casino will offer a coupon which can be redeemed for a free ace in blackjack. Other times the dealer will start to deal and you can see the first card, before she pauses because you forgot to put out a bet. The following tables shows the value of each initial player card, accross whether the dealer hits (H17) or stands (S17) on a soft 17. The table is based on an infinite number of decks. In Basic Blackjack in table 32 (page 124) author Stanford Wong also gives the value of each initial player card based on six decks. The most Wong and I disagree is 0.3%, probably due to the number of decks.

### Free Card Value

Card S17 H17
ace 0.504019 0.501844
2 -0.132947 -0.133987
3 -0.153950 -0.154469
4 -0.176969 -0.177029
5 -0.196529 -0.196668
6 -0.209834 -0.209714
7 -0.180796 -0.182900
8 -0.084058 -0.090196
9 -0.009417 -0.013236
10 0.143489 0.140328

For example if you had a free ace coupon for a \$10 bet, and the dealer stands on soft 17, then the value of the coupon would be \$10 × 0.504019 = \$5.04.