Last Updated: August 8, 2019

# Joker Bet

## Introduction

Joker Bet is game of luck that goes through a 54-card deck, one card at a time. Before each card, the player may make various bets, such as the exact card, color, suit, and rank. The game can be found at TvBet, a supplier of live dealer games for Internet casinos.

## Rules

1. A standard 54-card deck is used, including one red and one black joker.
2. At the start of a round, the dealer deals one card off a shuffled deck.
3. The player may bet on any of the following on the next card in the deck:
• Exact card
• Rank
• Suit
• Color
• Either joker
• Number card (rank 2 to 10)
• Not a number card (J, Q, K, A, or Joker)
4. The dealer will reveal the next card in the deck and bets will be resolved automatically.
5. Return to step 3 until there is only one card remaining.
6. The odds offered, which are expressed on a "for one" basis, on any given bet are re-calibrated after each card played.
7. Bets are not offered if impossible to win.

## Win Rounding

After much observation, I've concluded the following is how the game calculates what to pay any winning bet:

• If the probability of winning is 4.5% or less, the game will offer winning odds of 5*int(0.18/p).
• If the probability of winning are 4.5% to 9.0%, the game will offer winning odds of int(.9/p).
• If the probability of winning are 9.0% to 18.0%, the game will offer winning odds of 0.1*int(9/p).
• If the probability of winning are 18.0% or over, the game will offer winning odds of 0.01*int(90/p).

In other words, the game will calculate the odds before rounding to retain a 90% return. If this unrounded number is 20 or more, it rounds it down to the nearest 5. Otherwise, if this unrounded number is 10 or more, it rounds it down to the nearest integer. Otherwise, if this unrounded number is 5 or more, it rounds it down to the nearest one decimal place. Otherwise, it rounds the unrounded win down to the nearest two decimal places.

The expected return will have the following ranges, according to the probability of winning, as follows:

• Probability of winning 4.5% or less: 72.00% to 90.00% (this range is lowest with a probability of winning of 3.6%)
• Probability of winning 4.5% to 9.0%: 81.82% to 90.00% (this range is lowest with a probability of winning of 8.18%)
• Probability of winning 9.0% to 18.0%: 88.24% to 90.00% (this range is lowest with a probability of winning of 17.65%)
• Probability of winning 18.0% or more%: 89.60% to 90.00% (this range is lowest with a possible probability of winning of 80.00%)

## Suit Analysis

The following table shows, for an example shoe, the number of remaining cards in each suit plus jokers, the odds offered on each, and the expected return on each suit bet. In the "cards left" column, the numbers represent, in order, the number of remaining spades, clubs, diamonds, hearts, and jokers. In the "pays" column, the numbers represent, in order, the offered win, in order, on spades, clubs, diamonds, and hearts.

As the four return columns show, the game does a good job of calibrating the odds to achieve a 90% payback.

### Suit Bets

Last
Card
Played
Cards
Left
Clubs,
Diamonds,
Hearts,
Jokers)
Pays
Clubs,
Diamonds,
Hearts)
Return
Clubs
Return
Diamonds
Return
Hearts
Return
2c 13, 12, 13, 13, 2 3.66, 3.97, 3.66, 3.66 89.8% 89.9% 89.8% 89.8%
4s 12, 12, 13, 13, 2 3.9, 3.9, 3.6, 3.6 90.0% 90.0% 90.0% 90.0%
2s 11, 12, 13, 13, 2 4.17, 3.82, 3.53, 3.53 89.9% 89.9% 90.0% 90.0%
7h 11, 12, 13, 12, 2 4.09, 3.75, 3.46, 3.75 90.0% 90.0% 90.0% 90.0%
3h 11, 12, 13, 11, 2 4, 3.67, 3.39, 4 89.8% 89.9% 89.9% 89.8%
Ah 11, 12, 13, 10, 2 3.92, 3.6, 3.32, 4.32 89.8% 90.0% 89.9% 90.0%
Qh 11, 12, 13, 9, 2 3.84, 3.52, 3.25, 4.7 89.9% 89.9% 89.9% 90.0%
10c 11, 11, 13, 9, 2 3.76, 3.76, 3.18, 4.6 89.9% 89.9% 89.9% 90.0%
Jh 11, 11, 13, 8, 2 3.68, 3.68, 3.11, 5 90.0% 90.0% 89.8% 88.9%
9s 10, 11, 13, 8, 2 3.96, 3.6, 3.04, 4.95 90.0% 90.0% 89.8% 90.0%
10s 9, 11, 13, 8, 2 4.3, 3.51, 2.98, 4.83 90.0% 89.8% 90.0% 89.9%
Jc 9, 10, 13, 8, 2 4.2, 3.78, 2.91, 4.72 90.0% 90.0% 90.0% 89.9%
10d 9, 10, 12, 8, 2 4.1, 3.69, 3.07, 4.61 90.0% 90.0% 89.9% 90.0%
8c 9, 9, 12, 8, 2 4, 4, 3, 4.5 90.0% 90.0% 90.0% 90.0%
7s 8, 9, 12, 8, 2 4.38, 3.9, 2.93, 4.38 89.8% 90.0% 90.0% 89.8%
BJ 8, 9, 12, 8, 2 4.27, 3.8, 2.85, 4.27 89.9% 90.0% 90.0% 89.9%
10h 8, 9, 12, 7, 2 4.16, 3.7, 2.78, 4.75 89.9% 90.0% 90.0% 89.9%
8d 8, 9, 11, 7, 2 4.05, 3.6, 2.95, 4.62 90.0% 90.0% 90.0% 89.8%
5s 7, 9, 11, 7, 2 4.5, 3.5, 2.86, 4.5 90.0% 90.0% 90.0% 90.0%
4c 7, 8, 11, 7, 2 4.37, 3.82, 2.78, 4.37 90.0% 89.9% 90.0% 90.0%
3d 7, 8, 10, 7, 2 4.24, 3.71, 2.97, 4.24 89.9% 89.9% 90.0% 89.9%
Jd 7, 8, 9, 7, 2 4.11, 3.6, 3.2, 4.11 89.9% 90.0% 90.0% 89.9%
5h 7, 8, 9, 6, 2 3.98, 3.48, 3.1, 4.65 89.9% 89.8% 90.0% 90.0%
2h 7, 8, 9, 5, 2 3.85, 3.37, 3, 5.4 89.8% 89.9% 90.0% 90.0%
9h 7, 8, 9, 4, 2 3.72, 3.26, 2.9, 6.5 89.8% 89.9% 90.0% 89.7%
5d 7, 8, 8, 4, 2 3.6, 3.15, 3.15, 6.3 90.0% 90.0% 90.0% 90.0%
Qs 6, 8, 8, 4, 2 4.05, 3.03, 3.03, 6 90.0% 89.8% 89.8% 88.9%
Qc 6, 7, 8, 4, 2 3.9, 3.34, 2.93, 5.8 90.0% 89.9% 90.0% 89.2%
Ks 5, 7, 8, 4, 2 4.5, 3.21, 2.81, 5.6 90.0% 89.9% 90.0% 89.6%
Ac 5, 6, 8, 4, 2 4.32, 3.6, 2.7, 5.4 90.0% 90.0% 90.0% 90.0%
6c 5, 5, 8, 4, 2 4.14, 4.14, 2.59, 5.1 90.0% 90.0% 90.0% 88.7%
6s 4, 5, 8, 4, 2 4.95, 3.96, 2.48, 4.95 90.0% 90.0% 90.0% 90.0%
2d 4, 5, 7, 4, 2 4.72, 3.78, 2.7, 4.72 89.9% 90.0% 90.0% 89.9%
Js 3, 5, 7, 4, 2 6, 3.6, 2.57, 4.5 90.0% 90.0% 90.0% 90.0%
9d 3, 5, 6, 4, 2 5.7, 3.42, 2.85, 4.27 90.0% 90.0% 90.0% 89.9%
8h 3, 5, 6, 3, 1 5.4, 3.24, 2.7, 5.4 90.0% 90.0% 90.0% 90.0%
RJ 3, 5, 6, 3, 0 5.1, 3.06, 2.55, 5.1 90.0% 90.0% 90.0% 90.0%
8s 2, 5, 6, 3, 0 7.2, 2.88, 2.4, 4.8 90.0% 90.0% 90.0% 90.0%
4d 2, 5, 5, 3, 0 6.7, 2.7, 2.7, 4.5 89.3% 90.0% 90.0% 90.0%
Qd 2, 5, 4, 3, 0 6.3, 2.52, 3.15, 4.2 90.0% 90.0% 90.0% 90.0%
3c 2, 4, 4, 3, 0 5.8, 2.93, 2.93, 3.9 89.2% 90.0% 90.0% 90.0%
5c 2, 3, 4, 3, 0 5.4, 3.6, 2.7, 3.6 90.0% 90.0% 90.0% 90.0%
Ad 2, 3, 3, 3, 0 4.95, 3.3, 3.3, 3.3 90.0% 90.0% 90.0% 90.0%
Kc 2, 2, 3, 3, 0 4.5, 4.5, 3, 3 90.0% 90.0% 90.0% 90.0%
4h 2, 2, 3, 2, 0 4.05, 4.05, 2.7, 4.05 90.0% 90.0% 90.0% 90.0%
6h 2, 2, 3, 1, 0 3.6, 3.6, 2.4, 7.2 90.0% 90.0% 90.0% 90.0%
Kh 2, 2, 3, 0, 0 3.15, 3.15, 2.1, 0 90.0% 90.0% 90.0%
3s 1, 2, 3, 0, 0 5.4, 2.7, 1.8, 0 90.0% 90.0% 90.0%
As 0, 2, 3, 0, 0 0, 2.25, 1.5, 0 90.0% 90.0%
9c 0, 1, 3, 0, 0 0, 3.6, 1.2, 0 90.0% 90.0%

## Color Analysis

The following table shows, for an example shoe, the last card played as well as, for both colors:

• Number remaining
• Probability
• Pays
• Expected return

As the two return columns show, the game does a good job of calibrating the odds to achieve a 90% payback.

### Suit Bets

Last
Card
Played
Red
Cards
Left
Black
Cards
Left
Prob.
Red
Prob.
Black
Red
Pays
Black
Pays
Red
Return
Black
Return
2c 27 26 50.9% 49.1% 1.766 1.834 89.97% 89.97%
4s 27 25 51.9% 48.1% 1.733 1.872 89.98% 90.00%
2s 27 24 52.9% 47.1% 1.700 1.912 90.00% 89.98%
7h 26 24 52.0% 48.0% 1.730 1.875 89.96% 90.00%
3h 25 24 51.0% 49.0% 1.764 1.837 90.00% 89.98%
Ah 24 24 50.0% 50.0% 1.800 1.800 90.00% 90.00%
Qh 23 24 48.9% 51.1% 1.839 1.762 89.99% 89.97%
10c 23 23 50.0% 50.0% 1.800 1.800 90.00% 90.00%
Jh 22 23 48.9% 51.1% 1.840 1.760 89.96% 89.96%
9s 22 22 50.0% 50.0% 1.800 1.800 90.00% 90.00%
10s 22 21 51.2% 48.8% 1.759 1.842 90.00% 89.96%
Jc 22 20 52.4% 47.6% 1.718 1.890 89.99% 90.00%
10d 21 20 51.2% 48.8% 1.757 1.845 89.99% 90.00%
8c 21 19 52.5% 47.5% 1.714 1.894 89.99% 89.97%
7s 21 18 53.8% 46.2% 1.671 1.950 89.98% 90.00%
BJ 21 17 55.3% 44.7% 1.628 2.011 89.97% 89.97%
10h 20 17 54.1% 45.9% 1.665 1.958 90.00% 89.96%
8d 19 17 52.8% 47.2% 1.705 1.905 89.99% 89.96%
5s 19 16 54.3% 45.7% 1.657 1.968 89.95% 89.97%
4c 19 15 55.9% 44.1% 1.610 2.040 89.97% 90.00%
3d 18 15 54.5% 45.5% 1.650 1.980 90.00% 90.00%
Jd 17 15 53.1% 46.9% 1.694 1.920 89.99% 90.00%
5h 16 15 51.6% 48.4% 1.743 1.860 89.96% 90.00%
2h 15 15 50.0% 50.0% 1.800 1.800 90.00% 90.00%
9h 14 15 48.3% 51.7% 1.864 1.740 89.99% 90.00%
5d 13 15 46.4% 53.6% 1.938 1.680 89.98% 90.00%
Qs 13 14 48.1% 51.9% 1.869 1.735 89.99% 89.96%
Qc 13 13 50.0% 50.0% 1.800 1.800 90.00% 90.00%
Ks 13 12 52.0% 48.0% 1.730 1.875 89.96% 90.00%
Ac 13 11 54.2% 45.8% 1.661 1.963 89.97% 89.97%
6c 13 10 56.5% 43.5% 1.592 2.070 89.98% 90.00%
6s 13 9 59.1% 40.9% 1.523 2.200 90.00% 90.00%
2d 12 9 57.1% 42.9% 1.575 2.100 90.00% 90.00%
Js 12 8 60.0% 40.0% 1.500 2.250 90.00% 90.00%
9d 11 8 57.9% 42.1% 1.554 2.137 89.97% 89.98%
8h 10 8 55.6% 44.4% 1.620 2.025 90.00% 90.00%
RJ 9 8 52.9% 47.1% 1.700 1.912 90.00% 89.98%
8s 9 7 56.3% 43.8% 1.600 2.057 90.00% 89.99%
4d 8 7 53.3% 46.7% 1.687 1.928 89.97% 89.97%
Qd 7 7 50.0% 50.0% 1.800 1.800 90.00% 90.00%
3c 7 6 53.8% 46.2% 1.671 1.950 89.98% 90.00%
5c 7 5 58.3% 41.7% 1.542 2.160 89.95% 90.00%
Ad 6 5 54.5% 45.5% 1.650 1.980 90.00% 90.00%
Kc 6 4 60.0% 40.0% 1.500 2.250 90.00% 90.00%
4h 5 4 55.6% 44.4% 1.620 2.025 90.00% 90.00%
6h 4 4 50.0% 50.0% 1.800 1.800 90.00% 90.00%
Kh 3 4 42.9% 57.1% 2.100 1.575 90.00% 90.00%
3s 3 3 50.0% 50.0% 1.800 1.800 90.00% 90.00%
As 3 2 60.0% 40.0% 1.500 2.250 90.00% 90.00%
9c 3 1 75.0% 25.0% 1.200 3.600 90.00% 90.00%

## Number Bets

The following table shows, for an example shoe, the last card played as well as, for both numbers (2-10), and non-numbers (faces, aces, jokers):

• Number remaining
• Probability
• Pays
• Expected return

As the two return columns show, the game does a good job of calibrating the odds to achieve a 90% payback.

### Suit Bets

Last
Card
Played
Numbers
Left
Non-Numbers
Left
Prob.
Number
Prob.
Non-Number
Number
Pays
Non-Number
Pays
Number
Return
Non-Number
Return
2c 35 18 66.0% 34.0% 1.362 2.650 89.94% 90.00%
4s 34 18 65.4% 34.6% 1.376 2.600 89.97% 90.00%
2s 33 18 64.7% 35.3% 1.390 2.550 89.94% 90.00%
7h 32 18 64.0% 36.0% 1.406 2.500 89.98% 90.00%
3h 31 18 63.3% 36.7% 1.422 2.450 89.96% 90.00%
Ah 31 17 64.6% 35.4% 1.393 2.541 89.96% 89.99%
Qh 31 16 66.0% 34.0% 1.364 2.643 89.97% 89.97%
10c 30 16 65.2% 34.8% 1.380 2.587 90.00% 89.98%
Jh 30 15 66.7% 33.3% 1.350 2.700 90.00% 90.00%
9s 29 15 65.9% 34.1% 1.365 2.640 89.97% 90.00%
10s 28 15 65.1% 34.9% 1.382 2.580 89.99% 90.00%
Jc 28 14 66.7% 33.3% 1.350 2.700 90.00% 90.00%
10d 27 14 65.9% 34.1% 1.366 2.635 89.96% 89.98%
8c 26 14 65.0% 35.0% 1.384 2.571 89.96% 89.99%
7s 25 14 64.1% 35.9% 1.404 2.507 90.00% 89.99%
BJ 25 13 65.8% 34.2% 1.368 2.630 90.00% 89.97%
10h 24 13 64.9% 35.1% 1.387 2.561 89.97% 89.98%
8d 23 13 63.9% 36.1% 1.408 2.492 89.96% 89.99%
5s 22 13 62.9% 37.1% 1.431 2.423 89.95% 90.00%
4c 21 13 61.8% 38.2% 1.457 2.353 89.99% 89.97%
3d 20 13 60.6% 39.4% 1.485 2.284 90.00% 89.98%
Jd 20 12 62.5% 37.5% 1.440 2.400 90.00% 90.00%
5h 19 12 61.3% 38.7% 1.468 2.325 89.97% 90.00%
2h 18 12 60.0% 40.0% 1.500 2.250 90.00% 90.00%
9h 17 12 58.6% 41.4% 1.535 2.175 89.98% 90.00%
5d 16 12 57.1% 42.9% 1.575 2.100 90.00% 90.00%
Qs 16 11 59.3% 40.7% 1.518 2.209 89.96% 90.00%
Qc 16 10 61.5% 38.5% 1.462 2.340 89.97% 90.00%
Ks 16 9 64.0% 36.0% 1.406 2.500 89.98% 90.00%
Ac 16 8 66.7% 33.3% 1.350 2.700 90.00% 90.00%
6c 15 8 65.2% 34.8% 1.380 2.587 90.00% 89.98%
6s 14 8 63.6% 36.4% 1.414 2.475 89.98% 90.00%
2d 13 8 61.9% 38.1% 1.453 2.362 89.95% 89.98%
Js 13 7 65.0% 35.0% 1.384 2.571 89.96% 89.99%
9d 12 7 63.2% 36.8% 1.425 2.442 90.00% 89.97%
8h 11 7 61.1% 38.9% 1.472 2.314 89.96% 89.99%
RJ 11 6 64.7% 35.3% 1.390 2.550 89.94% 90.00%
8s 10 6 62.5% 37.5% 1.440 2.400 90.00% 90.00%
4d 9 6 60.0% 40.0% 1.500 2.250 90.00% 90.00%
Qd 9 5 64.3% 35.7% 1.400 2.520 90.00% 90.00%
3c 8 5 61.5% 38.5% 1.462 2.340 89.97% 90.00%
5c 7 5 58.3% 41.7% 1.542 2.160 89.95% 90.00%
Ad 7 4 63.6% 36.4% 1.414 2.475 89.98% 90.00%
Kc 7 3 70.0% 30.0% 1.285 3.000 89.95% 90.00%
4h 6 3 66.7% 33.3% 1.350 2.700 90.00% 90.00%
6h 5 3 62.5% 37.5% 1.440 2.400 90.00% 90.00%
Kh 5 2 71.4% 28.6% 1.260 3.150 90.00% 90.00%
3s 4 2 66.7% 33.3% 1.350 2.700 90.00% 90.00%
As 4 1 80.0% 20.0% 1.125 4.500 90.00% 90.00%
9c 3 1 75.0% 25.0% 1.200 3.600 90.00% 90.00%
7c 2 1 66.7% 33.3% 1.350 2.700 90.00% 90.00%
7d 1 1 50.0% 50.0% 1.800 1.800 90.00% 90.00%

## Rank and Single Card Analysis

The following table shows what a bet wins on a single card and on any rank according to how many cards are left in that rank (1 to 4). The win for one card in a rank is the same as that of betting on a single card. The right four column shows the expected return according to the number of winning cards.

### Rank and Single Card Analysis

Cards Left 1 Winning
Card Pays
2 Winning
Cards Pay
3 Winning
Cards Pay
4 Winning
Cards Pay
1 Winning
Card Ret.
2 Winning
Cards Ret.
3 Winning
Cards Ret.
4 Winning
Cards Ret.
53 45 15 11 84.91% 84.91% 83.02%
52 45 20 15 11 86.54% 76.92% 86.54% 84.62%
51 45 20 15 11 88.24% 78.43% 88.24% 86.27%
50 45 20 15 11 90.00% 80.00% 90.00% 88.00%
49 40 20 14 11 81.63% 81.63% 85.71% 89.80%
48 40 20 14 10 83.33% 83.33% 87.50% 83.33%
47 40 20 14 10 85.11% 85.11% 89.36% 85.11%
46 40 20 13 10 86.96% 86.96% 84.78% 86.96%
45 40 20 13 10 88.89% 88.89% 86.67% 88.89%
44 35 19 13 9.9 79.55% 86.36% 88.64% 90.00%
43 35 19 12 9.6 81.40% 88.37% 83.72% 89.30%
42 35 18 12 9.4 83.33% 85.71% 85.71% 89.52%
41 35 18 12 9.2 85.37% 87.80% 87.80% 89.76%
40 35 18 12 9 87.50% 90.00% 90.00% 90.00%
39 35 17 11 8.7 89.74% 87.18% 84.62% 89.23%
38 30 17 11 8.5 78.95% 89.47% 86.84% 89.47%
37 30 16 11 8.3 81.08% 86.49% 89.19% 89.73%
36 30 16 10 8.1 83.33% 88.89% 83.33% 90.00%
35 30 15 10 7.8 85.71% 85.71% 85.71% 89.14%
34 30 15 10 7.6 88.24% 88.24% 88.24% 89.41%
33 25 14 9.9 7.4 75.76% 84.85% 90.00% 89.70%
32 25 14 9.6 7.2 78.13% 87.50% 90.00% 90.00%
31 25 13 9.3 6.9 80.65% 83.87% 90.00% 89.03%
30 25 13 9 6.7 83.33% 86.67% 90.00% 89.33%
29 25 13 8.7 6.5 86.21% 89.66% 90.00% 89.66%
28 25 12 8.4 6.3 89.29% 85.71% 90.00% 90.00%
27 20 12 8.1 6 74.07% 88.89% 90.00% 88.89%
26 20 11 7.8 5.8 76.92% 84.62% 90.00% 89.23%
25 20 11 7.5 5.6 80.00% 88.00% 90.00% 89.60%
24 20 10 7.2 5.4 83.33% 83.33% 90.00% 90.00%
23 20 10 6.9 5.1 86.96% 86.96% 90.00% 88.70%
22 19 9.9 6.6 4.95 86.36% 90.00% 90.00% 90.00%
21 18 9.4 6.3 4.72 85.71% 89.52% 90.00% 89.90%
20 18 9 6 4.5 90.00% 90.00% 90.00% 90.00%
19 17 8.5 5.7 4.27 89.47% 89.47% 90.00% 89.89%
18 16 8.1 5.4 4.05 88.89% 90.00% 90.00% 90.00%
17 15 7.6 5.1 3.82 88.24% 89.41% 90.00% 89.88%
16 14 7.2 4.8 3.6 87.50% 90.00% 90.00% 90.00%
15 13 6.7 4.5 3.37 86.67% 89.33% 90.00% 89.87%
14 12 6.3 4.2 3.15 85.71% 90.00% 90.00% 90.00%
13 11 5.8 3.9 2.92 84.62% 89.23% 90.00% 89.85%
12 10 5.4 3.6 2.7 83.33% 90.00% 90.00% 90.00%
11 9.9 4.95 3.3 2.47 90.00% 90.00% 90.00% 89.82%
10 9 4.5 3 2.25 90.00% 90.00% 90.00% 90.00%
9 8.1 4.05 2.7 2.02 90.00% 90.00% 90.00% 89.78%
8 7.2 3.6 2.4 1.8 90.00% 90.00% 90.00% 90.00%
7 6.3 3.15 2.1 1.57 90.00% 90.00% 90.00% 89.71%
6 5.4 2.7 1.8 1.35 90.00% 90.00% 90.00% 90.00%
5 4.5 2.25 1.5 1.12 90.00% 90.00% 90.00% 89.60%
4 3.6 1.8 1.2 0 90.00% 90.00% 90.00%
3 2.7 1.35 0 90.00% 90.00%
2 1.8 0 90.00%