# 2 3 5 Stud Poker

## Introduction

2 3 5 Stud Poker(™) is a poker variant I first saw at the 2022 Global Gaming Expo. Later, on June 13, 2023, I saw it on field trial at the Plaza casino in Las Vegas.

The player is paid based on his cards only. The betting structure is two raise or check decisions as cards are revealed.

2 3 5 Stud Poker is trademarked by Light and Wonder.

## Rules

1. A single 52-card deck is used.
2. Player makes three equal wagers labeled 2 Card Poker, 3 Card Poker, and 5 Card Poker. The player may make the optional Win 'Em All side bet at this time as well.
3. The dealer shall deal the player two cards, which he may examine.
4. The player may raise his 3 Card Poker bet by an amount equal to the original 3 Card Poker bet or check.
5. The dealer shall deal the player a third card, which he may examine.
6. The player may raise his 5 Card Poker bet by an amount equal to the original 5 Card Poker bet or check.
7. The dealer shall deal two community cards, which the player may use to make his best five-card hand.
8. All three required wagers shall pay according to the player's hand after two card, three cards, and all five cards per the pay tables below.
9. The Win 'Em All wager shall win if the player wins all three of the required bets and pay 12 to 1.

Event Pays
Pair 1
Straight 1
Flush 1

### 3 Card Poker Pay Table

Event Pays
Mini royal 50
Straight flush 20
Three of a kind 10
Straight 5
Flush 3
Pair 1

### 5 Card Poker Pay Table

Event Pays
Royal flush 500
Straight flush 250
Four of a kind 100
Full house 25
Flush 20
Straight 15
Three of a kind 7
Two pair 3
Pair 10's+ 1

## Analysis

The following table shows my analysis of the 2 Card Poker bet. The lower right cell shows a house edge of 17.65%.

### 2 Card Poker Return Table

Event Pays Combinations Probability Return
Win 1 546 0.411765 0.411765
Loss -1 780 0.588235 -0.588235
Total   1326 1.000000 -0.176471

The following table shows my analysis of the 3 Card Poker bet. The lower right cell shows a player edge of 1.92%. The probability the player will raise the 3 Card Poker bet is 39.37%.

### 3 Card Poker Return Table

Event Action Pays Combinations Probability Return
Mini Royal Raise 100 12 0.000181 0.018100
Straight flush Raise 40 132 0.001991 0.079638
Three of a kind Raise 20 156 0.002353 0.047059
Straight Raise 10 1,488 0.022443 0.224434
Flush Raise 6 3,288 0.049593 0.297557
Pair Raise 2 6,408 0.096652 0.193303
Loser Raise -2 14,616 0.220452 -0.440905
Mini Royal Check 50 0 0.000000 0.000000
Straight flush Check 20 0 0.000000 0.000000
Three of a kind Check 10 0 0.000000 0.000000
Straight Check 5 672 0.010136 0.050679
Flush Check 3 0 0.000000 0.000000
Pair Check 1 4,824 0.072760 0.072760
Loser Check -1 34,704 0.523439 -0.523439
Total     66,300 1.000000 0.019186

The following table shows my analysis of the 5 Card Poker bet. The lower right cell shows a player edge of 9.78%. The probability the player will raise the 5 Card Poker bet is 26.43%.

### 5 Card Poker Return Table

Event Action Pays Combinations Probability Return
Royal flush Raise 1000 120 0.000002 0.001539
Straight flush Raise 500 1,080 0.000014 0.006926
Four of a kind Raise 200 18,720 0.000240 0.048019
Full house Raise 50 112,320 0.001441 0.072029
Flush Raise 40 153,240 0.001965 0.078616
Straight Raise 30 95,760 0.001228 0.036846
Three of a kind Raise 14 1,208,340 0.015498 0.216968
Two pair Raise 6 2,389,500 0.030647 0.183881
Tens or better Raise 2 5,237,280 0.067171 0.134343
Loser Raise -2 11,387,160 0.146048 -0.292095
Royal flush Check 500 0 0.000000 0.000000
Straight flush Check 250 0 0.000000 0.000000
Four of a kind Check 100 0 0.000000 0.000000
Full house Check 25 0 0.000000 0.000000
Flush Check 20 0 0.000000 0.000000
Straight Check 15 210,240 0.002696 0.040447
Three of a kind Check 7 439,020 0.005631 0.039415
Two pair Check 3 1,317,060 0.016892 0.050676
Tens or better Check 1 7,434,720 0.095355 0.095355
Loser Check -1 47,964,240 0.615172 -0.615172
Total     77,968,800 1.000000 0.097793

The following table shows the expected value of all three poker bets.

### 2-3-5 Poker Summary

Bet Expected
Value
Expected
Bet
2 Card Poker -0.176471 1.000000
3 Card Poker 0.019186 1.393665
5 Card Poker 0.097793 1.264253
Total -0.059492 3.657919

The table above shows that if the player bets one unit on each of the three poker bets, he can expect to lose 0.059492 units. If we define the house edge as the ratio of the expected loss to one unit, we get 5.95%. If we define it as the ratio of the expected loss to the sum of the required initial bets, we get 0.059492/3 = 1.98%.

The lower right cell shows that after raising, the average final wager is 3.657919. The ratio of the expected loss to the total amount wagered, known as the element of risk, we get 0.059492/3.657919 = 1.63%.

The following table shows my analysis of the Win 'Em All bet. The lower right cell shows a house edge of 7.39%.

### Win 'Em All

Event Pays Combinations Probability Return
Win 12 5554368 0.071238 0.854860
Loss -1 72414432 0.928762 -0.928762
Total   77968800 1.000000 -0.073902

## Strategy

The player should raise the 3 Card Poker bet with any of the following in the first two cards.

• Any pair
• Any two to a straight flush
• Open-ended straight draw

The player should raise the 5 Card Poker bet with any of the following in the first three cards.

• Any pair or three of a kind
• Any three suited cards
• Three to a straight with 0 gaps with at least one 10 or better (example 8-9-10).
• Three to a straight with 1 gap with at least two 10's or better (example 8-10-J).
• Any three to a straight all 10 or better (example 10-Q-A).