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EZ Bust

Introduction

The EZ Bust is among the various side bets in blackjack that wins if the dealer goes bust. Players can place their bet after the dealer shows their up card. The EZ Bust bet is only available against a dealer showing a card from 2 to 6, and it pays out at even money.

Rules

  1. This side bet follows the standard rules of blackjack.
  2. The dealer exposes his up card.
  3. If the dealer's up card falls between 2 to 6, players are presented with the opportunity to place the Bet the Bust side bet.
  4. Should the player opt for this bet and the dealer ends up busting, the EZ Bust wager pays out even money.
  5. A rule that remains uncertain is whether the dealer will still complete their hand if every player at the table has busted. This report operates under the assumption that the dealer does continue to deal.

Analysis

The subsequent table illustrates the likelihood of the dealer busting based on the up card listed in the left column, with the number of decks represented across the top. This table is created under the condition that the dealer stands on a soft 17.

Probability of the Dealer Busting -- Dealer Stands on Soft 17

Up Card 1 Decks 2 Decks 4 Decks 6 Decks 8 Decks
A 0.169815 0.168096 0.167557 0.167293 0.167136
2 0.352973 0.353291 0.353398 0.353451 0.353483
3 0.375588 0.374794 0.374501 0.374349 0.374256
4 0.402803 0.398540 0.397162 0.396481 0.396075
5 0.428905 0.422505 0.420440 0.419419 0.418810
6 0.420823 0.422132 0.422503 0.422676 0.422776
7 0.259854 0.261143 0.261546 0.261742 0.261859
8 0.238627 0.241630 0.242656 0.243173 0.243485
9 0.233442 0.230898 0.230066 0.229653 0.229406
10 0.232499 0.231144 0.230692 0.230465 0.230329

The upcoming table shows the expected return from the EZ Bust bet with the up card in the left column and the number of decks at the top. It assumes the dealer stands on a soft 17.

Expected Return -- Dealer Stands on Soft 17

Up Card 1 Decks 2 Decks 4 Decks 6 Decks 8 Decks
2 -0.294054 -0.293418 -0.293204 -0.293098 -0.293034
3 -0.248824 -0.250412 -0.250998 -0.251302 -0.251488
4 -0.194394 -0.202920 -0.205676 -0.207038 -0.207850
5 -0.142190 -0.154990 -0.159120 -0.161162 -0.162380
6 -0.158354 -0.155736 -0.154994 -0.154648 -0.154448

The following table displays the probability of the dealer busting based on their up card in the left column and the number of decks in the top row, assuming the dealer hits on a soft 17.

Probability of Dealer Busting -- Dealer Hits on Soft 17

Up Card 1 Decks 2 Decks 4 Decks 6 Decks 8 Decks
2 0.356345 0.356527 0.356593 0.356627 0.356647
3 0.378075 0.377460 0.377218 0.377090 0.377011
4 0.405796 0.401328 0.399887 0.399176 0.398751
5 0.429961 0.423668 0.421634 0.420629 0.420030
6 0.437756 0.438754 0.439022 0.439144 0.439214

The next table outlines the expected return for the Bet the Bust wager, with the up card indicated in the left column and the number of decks across the top, predicated on the dealer hitting on a soft 17.

Expected Return -- Dealer Hits on Soft 17

Up Card 1 Decks 2 Decks 4 Decks 6 Decks 8 Decks
2 -0.287310 -0.286946 -0.286814 -0.286746 -0.286706
3 -0.243850 -0.245080 -0.245564 -0.245820 -0.245978
4 -0.188408 -0.197344 -0.200226 -0.201648 -0.202498
5 -0.140078 -0.152664 -0.156732 -0.158742 -0.159940
6 -0.124488 -0.122492 -0.121956 -0.121712 -0.121572

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Written by: Michael Shackleford