The following Excel spreadsheet simulates the dealing of 6 decks of cards at random. It graphs the running count, true count, and player advantage as the cards are dealt. When counting cards, you should make your minimum waiting bet when the player advantage is zero or negative. When the player advantage goes positive, you should bet a percentage of your bankroll equal to your player advantage, according to the Kelly Criterion.

## Instructions

- If you don't see the following graphs, use the spreadsheet scroll bars to bring them into view:

- Running count / True count
- Player advantage %
- To deal another 6 decks and update the graphs, click the Refresh icon ( ) at the bottom of the spreadsheet, or reload the page.

## Notes

- To see graphs for a single-deck or double-deck game, click the "Single" or "2 decks" tab at the bottom of the window.

- If you accidentally modify a cell value or formula, you might ruin the graph. To fix it, reload the web page.

- An alternative way to deal 6 decks is to press the F9 key. However, you first need to select any cell in the spreadsheet, such as cell K4.

- Some ad blockers prevent loading of the spreadsheet. In that case, temporarily disable your ad blocker.

## Instructional Videos

Running Count

True Count

Two Decks

Six Decks 3:2 6:5

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## Running Count / True Count Graph

The running count (grey graph line) keeps track of the number of high vs. low cards using the classic Hi-Lo count strategy, where cards 2-3-4-5-6 have a value of +1, cards 7-8-9 have a value of 0, and cards 10-J-Q-K-A have a value of -1. The count at the beginning is zero. The count at the end is also zero, because the numbers of low and high cards are balanced.

As the cards are dealt, the count randomly varies between positive and negative values, depending on whether more low or high cards are dealt out. The graph is equally likely to be above or below zero.

The true count (blue graph line in top graph) is the running count divided by the number remaining decks to be dealt. This adjusts the running count to determine the true effect, fraction-wise, on the probability of dealing out high or low cards from the remaining decks. For this reason, I prefer to call this the "true-effectcount" or "one-deck equivalent count."

## Player Advantage Graph

The player advantage graph shows your advantage as a percentage of your bet. For example, when your advantage is 1.00 percent and you make a $20 bet, your average win on that bet will be 20 cents. Not a huge advantage by any means!

You have an advantage when the graph goes above zero, as indicated by the solid black horizontal line. The dashed horizontal purple line - - - - - - - represents the basic strategy player edge for a typical good 6-deck game, -0.6 percent. The player advantage graph is centered on the dashed purple line; it is equally likely to be above or below this line. Thus, you play at a disadvantage more than half the time.

The player advantage graph is shown solid for the first 4.5 decks and dashed for the remaining 1.5 decks. This is because most casinos shuffle when there are 1.5 decks remaining. That means you will not have any opportunities to make bets in the dashed portions of the graph.

You can place a bet only at the end of each round. At an uncrowded table, maybe 12 or so cards are dealt in each round, on average. Therefore, I've spaced the card number labels at the bottom at intervals of 12. These represent (approximately) the intervals at which you can place bets.

Cell N2 contains the basic strategy player advantage at the start of the game,-0.60percent by default. For a game that pays only 6:5 on blackjack, the player advantage is worse by 1.4 percent. To see the effect of a 6:5 payoff, enter-2.00into cell N2.

## Player Advantage Pie Chart

The pie chart shows the relative amounts of time that you play at an advantage, at a disadvantage, and even with the casino. A player edge between -0.25 and +0.25 percent is considered even. The pie chart applies only to the part of the graph before the shuffle.

## For More Information

Kelly Criterion Simulation, Optimum Bet Size for Bankroll Growth

(DIY Kelly bet size simulator for 1,000 bets)

For more about card counting, see Does Card Counting Really Work? (web page or YouTube video)

Or see the whole YouTube playlist "Easy basic strategy, house edge, and card counting"

For another good introduction to card counting, see The Wizard of Odds website

For a very good and free online book on blackjack, see Modern Blackjack, An Illustrated Guide to Blackjack Advantage Play, by Norman Wattenberger

For a detailed technical look at the game, see Wattenberger's How Blackjack Works

©2019 G Chang, BlackjackCalculation.com

Questions or Comments? email: BlackjackCalculation [at] gmail [dot] com

OK for personal use. Please do not share or post the spreadsheet. Direct others to this web page.