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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
- The player must make five identical bets, one on each of four blackjack hands and one on the Four 20's side bet.
- 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
- 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
- The side bet is adjudicated before the dealer peeks for blackjack.
- 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.
External Links
- Discussion about Four 20's blackjack in my forum at Wizard of Vegas.
- Demo of Four 20's blackjack at the Draft Kings web site.