Last Updated: April 18, 2018

# Poker Bo

## Introduction

Poker Bo is a simple poker-based game in which the player bets on the poker-value of five cards dealt from a six-deck shoe. Much like roulette, there are not decisions to make, other than bet selection.

As of this writing, in April 2018, it can be found at the Crown casino in Melbourne.

## Rules

The following rules assume the reader already knows the definitions of the various poker hands.

1. Six decks of ordinary cards are used.
2. Various bets are available, as follows, on the poker value of a randomly drawn five-card hand.
3. The Straight 'n' Up bet pays based on the highest poker value of the hand. In the event the hand qualifies for multiple wins, only the higher/highest ranking poker hand shall apply.
4. The Three of a Kind bet shall pay 20 to 1 if the poker value of the hand is a three of a kind, including a hand that can be scored as both a flush and three of a kind. It will not pay on a full house, four of a kind, or five of a kind.
5. The Two Pair bet shall pay 13 to 1 if the poker value of the hand is a two pair, including a hand that can be scored as both a flush and two pair. It will not pay on a full house, four of a kind, or five of a kind.
6. The Pair bet shall pay 1 to 1 if the poker value of the hand is a pair, including a hand that can be scored as both a flush and pair. It will not pay on a two pair, three of a kind, full house, four of a kind, or five of a kind.
7. The No Hand bet shall pay if the poker value of the hand is ace high or less.
8. There are four Specific Suit bets, one for each suit. Each pays according to the number of cards in the chosen suit in the five-card poker hand.

## Analysis

The following table shows my analysis of the Straight 'n' Up bet. The lower right cell shows a house edge of 10.11%.

### Straight 'n' Up

Event Pays Combinations Probability Return
Royal flush 500 31,104 0.000001 0.000652
Straight flush 400 279,936 0.000012 0.004694
Five of a kind 300 552,552 0.000023 0.006948
Four of a kind 150 39,783,744 0.001668 0.250145
Full house 100 87,145,344 0.003653 0.365291
Flush 50 83,889,648 0.003516 0.175822
Straight 25 79,315,200 0.003325 0.083117
All other -1 23,565,387,024 0.987802 -0.987802
Total 23,856,384,552 1.000000 -0.101132

The following table shows my analysis of the Three of a Kind bet. The lower right cell shows a house edge of 11.95%.

### Three of a Kind

Event Pays Combinations Probability Return
Three of a kind 20 1,000,276,992 0.041929 0.838582
All other -1 22,856,107,560 0.958071 -0.958071
Total 23,856,384,552 1.000000 -0.119489

The following table shows my analysis of the Two Pair bet. The lower right cell shows a house edge of 7.95%.

### Two Pair

Event Pays Combinations Probability Return
Two pair 13 1,568,616,192 0.065752 0.854782
All other -1 22,287,768,360 0.934248 -0.934248
Total 23,856,384,552 1.000000 -0.079465

The following table shows my analysis of the Pair bet. The lower right cell shows a house edge of 8.52%.

### Pair

Event Pays Combinations Probability Return
Pair 1 10,912,112,640 0.457408 0.457408
All other -1 12,944,271,912 0.542592 -0.542592
Total 23,856,384,552 1.000000 -0.085183

The following table shows my analysis of the No Hand bet. The lower right cell shows a house edge of 15.09%.

### No Hand

Event Pays Combinations Probability Return
No hand 1 10,128,551,040 0.424564 0.424564
All other -1 13,727,833,512 0.575436 -0.575436
Total 23,856,384,552 1.000000 -0.150873

The following table shows my analysis of the four Specific Suit bets. The number column reflects the number of cards in the chosen suit in the five-card hand. The lower right cell shows a house edge of 7.94%.

### Specific Suit

Number Pays Combinations Probability Return
5 50 21,111,090 0.000885 0.044246
4 5 333,783,450 0.013991 0.069957
3 2 2,073,907,836 0.086933 0.173866
2 1 6,330,876,552 0.265375 0.265375
1 or 0 -1 15,096,705,624 0.632816 -0.632816
Total 23,856,384,552 1.000000 -0.079373