# Four 20's

## Introduction

Four 20's is not just the police code for possession of marijuana, but also a blackjack game by DraftKings. The proper name for the game is Four 20s Blackjack, but I am treating it as a side bet, which I'm calling Four 20's. It plays like conventional four-hand blackjack, except mandates a side bet. The side bet pays according to the number of 20's the player gets in his first four hands.

## Rules

1. The player must make five identical bets, one on each of four blackjack hands and one on the Four 20's side bet.
2. The blackjack rules are as follows:
• Eight decks
• Dealer stands on soft 17
• Blackjack pays 3 to 2
• Dealer peeks for blackjack
• Player may double on any two cards
• Player may double after a split
• Player may re-split any pair, except aces, up to four hands
• Split aces get one card only per hand
• Surrender is not allowed
3. The Four 20's side bet pays based on how many hands of 20 points the player gets in his initial two cards per hand. Both hard and soft (ace/9) 20's count. The pay table is as follows:
• Four 20's pays 420 to 1
• Three 20's pays 20 to 1
• Two 20's pays 4 to 1
• One 20 pays a random win from a push to 3 to 1
4. The side bet is adjudicated before the dealer peeks for blackjack.
5. If the player gets one 20, then a spinning wheel will determine the win. The following are the possible outcomes and probabilities for the prize wheel.
• 3x: 5%
• 2x: 15%
• 1x: 50%
• Push (wheel stops on line): 30%

## Analysis

The following table shows the possible outcome of the win wheel for one 20. The lower right cell shows the average win for one 20 is 95.00% of the bet amount (on a "for one" basis).

### One 20 Wheel

Win Weight Probability Return
3 1 0.05 0.15
2 3 0.15 0.30
1 10 0.50 0.50
0 6 0.30 0.00
Total 20 1.00 0.95

The following table shows the number of combinations, probability, and contribution to the return for all possible outcomes from 0 to 4 of the total hands with 20 points. An average win is shown for one 20. The lower right cell shows a house advantage of 0.42%.

### Summarized Return Table

20's Pays Permutations Probability Return
4 420 96,154,845,853,132,800 0.000115 0.048182
3 20 3,423,358,427,452,540,000 0.004084 0.081685
2 4 44,788,356,273,817,700,000 0.053435 0.213741
1 0.95 255,238,297,847,250,000,000 0.304514 0.289289
0 -1 534,635,239,424,785,000,000 0.637851 -0.637851
Total   838,181,406,819,158,000,000 1.000000 -0.004955

The next table is a detailed return table, breaking down the possible wins for one 20.

### Detailed Return Table

20's Pays Weight Probability Return
Four 20's 420 1,923,096,917,062,660,000 0.000115 0.048182
Three 20's 20 68,467,168,549,050,800,000 0.004084 0.081685
Two 20's 4 895,767,125,476,354,000,000 0.053435 0.213741
One 20 -- 3x 3 255,238,297,847,250,000,000 0.015226 0.045677
One 20 -- 2x 2 765,714,893,541,749,000,000 0.045677 0.091354
One 20 -- 1x 1 2,552,382,978,472,500,000,000 0.152257 0.152257
One 20 -- Push 0 1,531,429,787,083,500,000,000 0.091354 0.000000
Zero 20's -1 10,692,704,788,495,700,000,000 0.637851 -0.637851
Total   16,763,628,136,383,200,000,000 1.000000 -0.004955

This page is intended to treat the Four 20's as a side bet, as opposed to a game. However, for those interested, my blackjack house edge calculator says the house edge in the Four 20s Blackjack base game is 0.43286%, based on basic strategy and shuffling the cards after every hand. This is line with the 0.42% house edge quoted in the game help file.