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Last Updated: August 15, 2016

Effect of Strategy Mismatches in Video Poker

Introduction

This has probably happened to many video poker players: you know one or two strategies but are in a situation where those games aren't available and you want to play another game. For example, you know 9-6 Jacks or Better strategy but the best game available is 9-6 Double Double Bonus. What will be the cost in errors due to the strategy mismatch?

Expected Values

The tables below show the return by optimal strategy for that game as well as for the optimal strategy for six well-known video poker games:

  • 9-6 Jacks or Better
  • 8-5 Bonus Poker
  • 10-7 Double Bonus
  • 9-6 Double Double Bonus
  • Full pay Deuces Wild (25-15-9-5-3)
  • Not so Ugly Ducks Deuces Wild (25-16-10-4-4)


There are some plays where the player is indifferent in one game but not in another. In some common sense situations, I assume the player will make some obvious adjustments, as follows:

  • If a player is playing a Jacks or Better, Bonus Poker, or Double Bonus strategy on a Double Double Bonus game, and is dealt four of a kind, then he will keep a good kicker (A to 4) and discard a bad kicker (5 to K). In Jacks or Better, Bonus Poker, or Double Bonus, the player would normally be indifferent to holding the kicker.
  • If a player is playing either of the Deuces Wild strategies on a Double Bonus Deuces Wild game, and is dealt four deuces, then he will keep a good kicker (ace) and discard a bad kicker (3 to K). In regular deuces wild, the player would normally be indifferent to holding the kicker.
  • If a player is playing the full pay deuces wild strategy on a Double Bonus Deuces Wild or Deuces Wild Bonus Poker game, and is dealt a two pair (where the strategy calls for holding just one of them), then he will favor holding aces first, followed by a 3-5, and finally 6-K. In full pay deuces wild, the player would normally be indifferent to holding either pair.


Expected Returns — Nothing Wild

Game Optimal 9-6
Jacks
8-5
Bonus
Poker
10-7
Double
Bonus
9-6
Double
Double
Bonus
9/6 Jacks 99.54% 99.54% 99.54% 98.94% 98.51%
9/5 Jacks 98.45% 98.44% 98.45% 97.44% 97.38%
8/6 Jacks 98.39% 98.39% 98.39% 97.82% 97.43%
8/5 Bonus Poker 99.17% 99.16% 99.17% 98.20% 98.37%
7/5 Bonus Poker 98.07% 98.01% 98.01% 97.08% 97.29%
10/6 Double Double Bonus 100.07% 99.76% 99.76% 99.57% 100.07%
9/6 Double Double Bonus 98.98% 98.61% 98.61% 98.45% 98.98%
9/5 Double Double Bonus 97.87% 97.51% 97.52% 96.96% 97.84%
8/5 Double Double Bonus 96.79% 96.36% 96.37% 95.84% 96.76%
10/7/5 Double Bonus 100.17% 99.63% 99.61% 100.17% 99.86%
9/7/5 Double Bonus 99.11% 98.48% 98.46% 99.05% 98.77%
9/6/5 Double Bonus 97.81% 97.38% 97.37% 97.56% 97.63%
9/6 Bonus Poker Deluxe 99.64% 99.61% 99.60% 99.29% 99.37%
9/7 Triple Double Bonus 99.58% 97.71% 97.69% 98.24% 98.49%
9/5 White Hot Aces 99.57% 99.16% 99.16% 98.59% 99.54%


The next table is for deuces wild games.

Expected Returns — Deuces Wild

Game Optimal Full Pay NSUD
Deuces Wild 25-15-9-5-3 100.76% 100.76% 99.73%
Deuces Wild 25-16-10-4-4 99.73% 98.80% 99.73%
Deuces Wild 25-15-9-4-4 98.91% 98.06% 98.90%
Deuces Wild 20-12-10-4-4 97.58% 96.62% 97.53%
Deuces Wild 25-16-13-4-3 96.77% 96.25% 96.58%
Deuces Wild Bonus Poker 9-4-4 99.45% 97.66% 98.18%
Deuces Wild Bonus Poker 13-4-3 98.80% 97.20% 97.62%
Deuces Wild Bonus Poker 10-4-3 97.36% 95.95% 96.08%
Double Bonus Deuces Wild 12-4-3 99.81% 98.10% 97.88%
Double Bonus Deuces Wild 9-4-3 98.61% 96.85% 96.34%


Cost of Errors

The next table shows the difference in return between optimal strategy and the strategy indicated in the top column.

Cost of Errors — Nothing Wild

Game 9-6
Jacks
8-5
Bonus
Poker
10-7
Double
Bonus
9-6
Double
Double
Bonus
9/6 JoB 0.00% 0.01% 0.61% 1.03%
9/5 JoB 0.01% 0.00% 1.01% 1.07%
8/6 JoB 0.00% 0.01% 0.57% 0.97%
8/5 BP 0.01% 0.00% 0.96% 0.79%
7/5 BP 0.06% 0.05% 0.99% 0.78%
10/6 DDB 0.30% 0.31% 0.50% 0.00%
9/6 DDB 0.37% 0.37% 0.53% 0.00%
9/5 DDB 0.36% 0.35% 0.92% 0.03%
8/5 DDB 0.43% 0.42% 0.95% 0.03%
10/7/5 DB 0.54% 0.56% 0.00% 0.32%
9/7/5 DB 0.63% 0.65% 0.05% 0.34%
9/6/5 DB 0.43% 0.43% 0.25% 0.17%
9/6 BPD 0.03% 0.04% 0.35% 0.28%
9/7 TDB 1.86% 1.88% 1.34% 1.09%
9/5 WHA 0.41% 0.41% 0.98% 0.03%


What does the table above show, in plain simple English? Here are some conclusions I've made.

  • There is generally not a big cost to a pay table mismatch. For example, the cost in mistakes for using 9-6 Jacks strategy on a 9-5 game is 0.01% only. An exception is using 10-7-5 Double Bonus strategy on a 9-6-5 game, where the error cost is 0.25%.
  • There is little cost to using Jacks or Better strategy in Bonus Poker or vise versa.
  • Bonus Poker Deluxe can be played with Jacks or Better/Bonus Poker strategy with little cost in errors.
  • There is a huge cost in playing any of the four strategies covered on Triple Double Bonus. I wouldn't touch that game unless you know the strategy specifically for it.


Cost of Errors — Deuces Wild

Game Full Pay NSUD
Deuces Wild 25-15-9-5-3 0.00% 1.03%
Deuces Wild 25-16-10-4-4 0.93% 0.00%
Deuces Wild 25-15-9-4-4 0.85% 0.01%
Deuces Wild 20-12-10-4-4 0.96% 0.05%
Deuces Wild 25-16-13-4-3 0.51% 0.18%
Deuces Wild Bonus Poker 9-4-4 1.79% 1.27%
Deuces Wild Bonus Poker 13-4-3 1.60% 1.18%
Deuces Wild Bonus Poker 10-4-3 1.41% 1.29%
Double Bonus Deuces Wild 12-4-3 1.70% 1.92%
Double Bonus Deuces Wild 9-4-3 1.76% 2.27%


Here are some thoughts on the deuces wild table above.

  • Do not use the Full Pay and NSUD (not so ugly ducks) strategy on each other.
  • The NSUD strategy is going to result in a lower error cost on more inferior pay tables than the full pay strategy. The full pay strategy should only be used on a full pay game (which are hard to find any longer at denominations over 25¢).
  • Deuces Wild Bonus Poker and Double Bonus Deuces Wild should not be played with any strategy for conventional deuces wild.


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Written by: Michael Shackleford

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