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Three Card Draw Poker

Introduction

Three Card Draw Poker is a variant of video poker that uses three cards instead of five and employs four decks. Players have the option to choose between different games such as 'sevens or better' and 'bonus poker'. Additionally, they can select from different payout options including three pay, five pay, and ten pay. I’ve observed that the machines typically allow multiple coins. Currently, I’ve spotted this game at venues like the Orleans and Caesars Palace.

Sevens or Better

The table below illustrates the payout structure and relevant statistics for the most favorable pay table I’ve encountered for Three Card Draw Poker. This particular variant can be played using $1 coins at Caesars Palace.

Probabilities Involved in Three Card Draw Poker – Sevens or Better

Hand Pays Combinations Probability Return
3 suited ace of spades 800 96215784 0.000015 0.012267
3 suited aces 160 280930104 0.000045 0.007163
3 of a kind suited 80 3390178176 0.00054 0.043223
AKQ suited 80 5213655552 0.000831 0.066471
3 aces 25 12822960192 0.002044 0.051089
Straight flush 12 41454171648 0.006606 0.079277
3 of a kind 5 87660405504 0.01397 0.069851
Straight 3 547919376384 0.087321 0.261962
Suited pair 2 415505124864 0.066218 0.132436
Flush 1 486173627904 0.07748 0.07748
Pair: 7-A 1 1116492023808 0.177933 0.177933
Nothing 0 3557788920960 0.566997 0
Total 6274797590880 1 0.979153

The subsequent pay table is accessible at both 25 and 50 cent denominations at Caesars Palace, as well as for 25 cents at the Orleans.

Probabilities Involved in Three Card Draw Poker – Sevens or Better

Hand Pays Combinations Probability Return
3 suited ace of spades 800 96215784 0.000015 0.012267
3 suited aces 160 280930104 0.000045 0.007163
3 of a kind suited 80 3390178176 0.00054 0.043223
AKQ suited 80 5213655552 0.000831 0.066471
3 aces 25 12822960192 0.002044 0.051089
Straight flush 12 41454171648 0.006606 0.079277
3 of a kind 4 87660405504 0.01397 0.055881
Straight 3 547919376384 0.087321 0.261962
Suited pair 2 415505124864 0.066218 0.132436
Flush 1 486173627904 0.07748 0.07748
Pair: 7-A 1 1116492023808 0.177933 0.177933
Nothing 0 3557788920960 0.566997 0
Total 6274797590880 1 0.965183

There’s another pay table available for 5 and 10 cent games at the Orleans.

Probabilities Involved in Three Card Draw Poker – Sevens or Better

Hand Pays Combinations Probability Return
3 suited ace of spades 800 95397288 0.000015 0.012163
3 suited aces 160 280930104 0.000045 0.007163
3 of a kind suited 80 3390178176 0.00054 0.043223
AKQ suited 80 5209290240 0.00083 0.066415
3 aces 25 12795131328 0.002039 0.050978
Straight flush 10 39875487744 0.006355 0.063549
3 of a kind 4 87660405504 0.01397 0.055881
Straight 3 544337637888 0.08675 0.260249
Suited pair 2 414294686208 0.066025 0.13205
Flush 1 517871405568 0.082532 0.082532
Pair: 7-A 1 1116650110464 0.177958 0.177958
Nothing 0 3532336930368 0.56294 0
Total 6274797590880 1 0.952162

All statistics in this section derive from the optimal strategy suggested by computer analysis. Below is a player strategy intended to offer effective guidance for various situations. This approach works well for both the 97.92% and 95.52% payout tables available for sevens or better. Players should prioritize the hands listed hierarchically below. For instance, if you are dealt a suited 3/4/J, it would be more advantageous to keep the 3/4 (which is two to a straight flush and has no gap) instead of maintaining the pat flush.

  1. Pat three aces or higher
  2. Two ace of spades
  3. Straight flush
  4. Suited aces, except spaded
  5. Straight, three of a kind
  6. Suited pair 2-K
  7. Ace pair, unsuited
  8. 2 to A/K/Q suited
  9. Pair 7-K, unsuited
  10. Two to a straight flush, no gap, except A/2
  11. Flush
  12. Two cards suited to a straight flush with one gap, such as A/2 and A/3
  13. Ace of spades
  14. Two sequential unsuited cards ranging from 6/7 to Q/K1
  15. Ace, except spades
  16. Queen
  17. King
  18. In scenarios where only high cards are present, it's typically best to choose the highest one. However, if more than one high card exists, retain the middle card if (1) it lies between 7 and K, (2) it’s suited alongside a lower card, and (3) there are two or more gaps between the lower and middle cards.
  19. Toss everything
Exceptions:
If the jack is a spade, prioritize holding the jack and queen over the ace of spades.

Here are some hands that you should decisively avoid playing:
  • A low pair
  • Two suited high cards with multiple gaps between them
  • Two unsuited high cards with one or more gaps
  • Unsuited king and ace

Bonus Poker

Here is the best pay table I've seen for bonus poker, which is available for $1 coins at Caesars Palace.

Probabilities Involved in Three Card Draw Poker - Bonus Poker

Hand Pays Combinations Probability Return
3 suited ace of spades 800 76966272 0.000012 0.009813
3 suited aces 400 246474600 0.000039 0.015712
3 of a kind suited: 2-4 160 432790200 0.000069 0.011036
3 of a kind suited: 5-K 80 3000735360 0.000478 0.038258
AKQ suited 50 4850072064 0.000773 0.038647
3 aces 20 12728839488 0.002029 0.040571
Straight flush 12 42015063552 0.006696 0.08035
3 of a kind 6 91409142528 0.014568 0.087406
Straight 3 553149769728 0.088154 0.264463
Suited pair 2 412959407616 0.065812 0.131625
Flush 1 482377843200 0.076875 0.076875
Pair: 7-A 1 1110135527424 0.17692 0.17692
Nothing 0 3561414958848 0.567574 0
Total 6274797590880 1 0.971675

This pay table can also be found using 25 and 50 cent denominations at Caesars Palace.

Probabilities Involved in Three Card Draw Poker - Bonus Poker

Hand Pays Combinations Probability Return
3 suited ace of spades 800 77132160 0.000012 0.009834
3 suited aces 400 246972264 0.000039 0.015744
3 of a kind suited: 2-4 160 433951416 0.000069 0.011065
3 of a kind suited: 5-K 80 3007163520 0.000479 0.03834
AKQ suited 50 4860688896 0.000775 0.038732
3 aces 20 12751400256 0.002032 0.040643
Straight flush 12 42126429696 0.006714 0.080563
3 of a kind 5 87660405504 0.01397 0.069851
Straight 3 554979956736 0.088446 0.265338
Suited pair 2 415336748544 0.066191 0.132383
Flush 1 485161499136 0.077319 0.077319
Pair: 7-A 1 1116155271168 0.177879 0.177879
Nothing 0 3551999971584 0.566074 0
Total 6274797590880 1 0.95769

Probabilities Involved in Three Card Draw Poker - Bonus Poker

Hand Pays Combinations Probability Return
3 suited ace of spades 800 77132160 0.000012 0.009834
3 suited aces 400 246972264 0.000039 0.015744
3 of a kind suited: 2-4 160 433951416 0.000069 0.011065
3 of a kind suited: 5-K 80 3007163520 0.000479 0.03834
AKQ suited 50 4860688896 0.000775 0.038732
3 aces 20 12751400256 0.002032 0.040643
Straight flush 12 42126429696 0.006714 0.080563
3 of a kind 4 87660405504 0.01397 0.055881
Straight 3 554979956736 0.088446 0.265338
Suited pair 2 415336748544 0.066191 0.132383
Flush 1 485161499136 0.077319 0.077319
Pair: 7-A 1 1116155271168 0.177879 0.177879
Nothing 0 3551999971584 0.566074 0
Total 6274797590880 1 0.94372

Probabilities Involved in Three Card Draw Poker - Bonus Poker

Hand Pays Combinations Probability Return
3 suited ace of spades 800 77132160 0.000012 0.009834
3 suited aces 400 246972264 0.000039 0.015744
3 of a kind suited: 2-4 160 433951416 0.000069 0.011065
3 of a kind suited: 5-K 80 3007163520 0.000479 0.03834
AKQ suited 50 4860688896 0.000775 0.038732
3 aces 20 12751400256 0.002032 0.040643
Straight flush 10 40599817728 0.00647 0.064703
3 of a kind 4 87660405504 0.01397 0.055881
Straight 3 550400120832 0.087716 0.263148
Suited pair 2 414191789568 0.066009 0.132018
Flush 1 517602003456 0.082489 0.082489
Pair: 7-A 1 1116155271168 0.177879 0.177879
Nothing 0 3526810874112 0.56206 0
Total 6274797590880 1 0.930475

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Strategies

Full-Pay Jacks or Better:

Full-Pay Deuces Wild:

Quick Quads:

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