# Bet the Bust

## Introduction

Bet the Bust is one of many blackjack side bets that wins if the dealer busts. In this one, the player can make the decision after the dealer exposes his up card. Naturally, the greater the chances of busting, the less the bet pays.

## Rules

1. The side bet is based on ordinary blackjack rules.
2. The dealer exposes his up card and gives players the chance to make the Bet the Bust side bet.
3. If the player makes the bet, and the dealer eventually busts, then the Bet the Bust wager will pay according to the dealer's up card and the pay table below. Pays are on a "to one" basis.
4. One rule I am not sure of is whether the dealer will deal out his hand if every player at the table busts. The math in this report is based on the assumption that he does.

Up Card Pays
A 3.5
2 1.5
3 1.5
4 1.0
5 1.0
6 1.0
7 2.5
8 3.0
9 3.0
10 3.0

## Analysis

The next table shows the probability of the dealer busting by the up card along the left column and number of decks along the top row. This table assumes the dealer stands on a soft 17.

### Probability of 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 next table shows the expected return of the Bet the Bust wager by the up card along the left column and number of decks along the top row. This table 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
A -0.235833 -0.243568 -0.245994 -0.247182 -0.247888
2 -0.117568 -0.116773 -0.116505 -0.116373 -0.116293
3 -0.061030 -0.063015 -0.063748 -0.064128 -0.064360
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
7 -0.090511 -0.086000 -0.084589 -0.083903 -0.083494
8 -0.045492 -0.033480 -0.029376 -0.027308 -0.026060
9 -0.066232 -0.076408 -0.079736 -0.081388 -0.082376
10 -0.070004 -0.075424 -0.077232 -0.078140 -0.078684

The next table shows the probability of the dealer busting by the up card along the left column and number of decks along the top row. This table assumes 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
A 0.204574 0.202556 0.201912 0.201595 0.201406
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
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 next table shows the expected return of the Bet the Bust wager by the up card along the left column and number of decks along the top row. This table assumes the dealer hits on a soft 17.

### Expected Return -- Dealer Hits on Soft 17

Up Card 1 Decks 2 Decks 4 Decks 6 Decks 8 Decks
A -0.079417 -0.088498 -0.091396 -0.092823 -0.093673
2 -0.109138 -0.108683 -0.108518 -0.108433 -0.108383
3 -0.054813 -0.056350 -0.056955 -0.057275 -0.057473
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
7 -0.090511 -0.086000 -0.084589 -0.083903 -0.083494
8 -0.045492 -0.033480 -0.029376 -0.027308 -0.026060
9 -0.066232 -0.076408 -0.079736 -0.081388 -0.082376
10 -0.070004 -0.075424 -0.077232 -0.078140 -0.078684