Video Poker Appendix 3 Answers

Introduction

Question 1

Q1: What is the standard deviation of one hand of 1-play jacks or better on a $1 machine with max coins?

Answer 1

A1: From the 9/6 table we see the standard deviation is 4.417542. Multiply this by the total bet and the standard deviation is 4.42 × 5 × $1 = $22.09.

 

Question 2

Q2: What is the standard deviation of one hand of 1-play jacks or better on a 25 cent machine with max coins?

Answer 2

A2: From the 9/6 table we see the standard deviation is 4.417542. Multiply this by the coinage and the standard deviation is 4.42 × 25¢ × 5 = $5.52.

 

Question 3

Q3: What is the standard deviation of 10 hands of 1-play jacks or better on a 25 cent machine with max coins?

Answer 3

A3: From the 9/6 table we see the standard deviation per hand is 4.417542. Multiply this by the square root of the number of hands and the amount bet per hand and the standard deviation is 4.42 × sqrt(10) × 5 × $0.25 = $17.46.

 

Question 4

Q4: What is the standard deviation of 1 initial hands of 10-play jacks or better on a 25¢ machine with max coins?

 

Answer 4

A4: From the 9/6 table we see the standard deviation per final hand is 6.100180. Multiply this by the square root of the number of hands and the coinage and the standard deviation is 6.10 × 10^1/2 × 25c × 5 = $24.11.

 

Question 5

Q5: What is the standard deviation of 100 initial hands of 50-play deuces wild on a $5 machine with max coins?

 

Answer 5

A5: From the deuces wild table we see the standard deviation per final hand is 13.405118. Multiply this by the square root of the number of hands and the coinage and the standard deviation is 13.41 × sqrt(100 × 50) × $5 × 5 = $23,697.12.

 

Question 6

Q6: What is the standard deviation of 50 initial hands of 100-play deuces wild on a $5 machine with max coins?

Answer 6

A6: From the deuces table we see the standard deviation per final hand is 18.349382. Multiply this by the square root of the number of hands and the coinage and the standard deviation is 18.35 × sqrt(100 × 50) × $5 × 5 = $32,437.43.

 

Question 7

Q7: What is the standard deviation of 1 initial hand of 8-play 10/7 double bonus on a $2 machine with max coins?

 

Answer 7

A7: From the top table we see the variance of the deal is 3.391375 and the variance of the draw is 24.864165. The total variance in 8-play would be 8 × 3.391375 + 24.864165 = 51.9952. The standard deviation is the square root of that, or 7.2108. So the standard deviation of 8 such final hands is sqrt(8) × 7.2108 × $2 × 5 = $203.95.

 

Question 8

Q8: What is the standard deviation of 2000 initial hands of 23-play double bonus on a $25 machine with max coins?

 

Answer 8

A8: From the top table we see the variance of the deal is 3.391375 and the variance of the draw is 24.864165. The total variance in 23-play would be 23 × 3.391375 + 24.864165 = 102.8658. The standard deviation is the square root of that, or 10.1423. So the standard deviation of 2000 initial hands is sqrt(2000 × 23) × 10.1423 × $25 × 5 = $271,909.52.

 

For another good source on this subject visit Jazbo's article An Analysis of N-Play Video Poker. The articles includes variance breakdowns for 13 video poker variations.

Written by: Michael Shackleford