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Blackjack Odds and Understanding Probability

blackjack odds

Knowing the blackjack odds will make you a better player and hopefully beat the odds when playing at an online casino. If you want to apply any gambling strategy successfully you need to know the odds of the game you’re playing. It goes without saying but we’ll say it anyway: the odds are always in favor of the house. How else do you think they can create billion dollar mega-casinos in Las Vegas? The Blackjack rules are carefully structured to ensure a house edge. But just how heavily are the Blackjack odds weighed in favor of the house? If you’re a smart player, you know the house edge not as great as one might think – and certainly not insurmountable. You will be able to calculate the following:

  1. Blackjack Rule Variations
  2. Odds of busting
  3. Player advantage VS dealer upcard

Blackjack Rule Variations

If you want to be serious about playing blackjack you need to be able to calculate you odds for the game you’re playing. The blackjack odds depend on the different types of rule variations. Some online blackjack sites can be unclear about this so you need to pay attention. You can also adjust your blackjack strategy according to these rules. The following table shows the effect that rule variations have on the player’s expected return after taking the proper strategy adjustments. These changes are relative to the standard Atlantic City rules which results in a player’s expected return of -0.43%: 8 decks, dealer stands on soft 17, player can double on any first 2 cards, the player may double after splitting and the player may split to 4 hands. I will explain some of the rule variations under the table.

Rule Variations Effect
Five Card Charlie +1.46%
Player 21-points is automatic winner +0.54%
Early surrender against ace +0.39%
Early surrender against ten +0.24%
Player may double on any number of cards +0.23%
Player may draw to split aces +0.19%
Six card Charlie +0.16%
Player may resplit aces +0.08%
Late surrender against ten +0.07%
Seven card Charlie +0.01%
Late surrender against ace +0.00%
Split to only 2 hands -0.01%
No-peek: ace showing -0.01%
Player may double on 9-10-11 only -0.09%
No-peek ten showing -0.10%
Player may not resplit -0.10%
Player may not double after splitting -0.14%
Player may double on 10-11 only -0.18%
Blackjack pays 6-5 -1.39%
Player loses 17 ties -1.87%
Blackjack pays 1 to 1 -2.27%
Player loses 17-18 ties -3.58%
Player loses 17-19 ties -5.30%
Player loses 17-20 ties -8.38%
Player loses 17-21 ties -8.86%
Dealer bust on 22 is a push -9.53%

Five, six and seven card Charlie: a Charlie is an automatic winner, so in a six card Charlie the player wins on any six card hand that didn’t bust.

No-peek rule: The dealer doesn’t peek to see if he has blackjack.

How to calculate? You start with the basic Atlantic City rules (-0.43%) and take the rule variations according to the game you are playing to calculate the effect it has on the expected return. For example “Player may double on any number of cards” (+0.23%) and “Player may not resplit” (-0.10%). The expected player return would now be -0.43% +0.23% -0.10%= -0.30%. These blackjack odds (-0.30%) are better for the player then under the standard Atlantic City rules (-0.43).

Blackjack Odds of busting

This table is used to calculate the blackjack odds of the player busting if he hits. This can be useful but I think a smart person already knows that if he hits on 16 he has more chances of busting when he hits on 12.

Hand % Bust if hit
21 100%
20 92%
19 85%
18 77%
17 69%
16 62%
15 58%
14 56%
13 39%
12 31%
11 or less 0%

Player advantage VS the dealers upcard

This table is more useful then the odds of busting, because it calculates how much the dealers upcard has a positive effect on your odds and the odds of him/her (the dealer) busting.

Dealer up Card Dealer bust % Player Advantage %
2 35.32% 9.5%
3 37.58% 13.6%
4 40.27% 18.4%
5 42.88% 23.1%
6 42.10% 23.8%
7 26.00% 14.6%
8 23.84% 5.4%
9 23.34% -4.4%
10,J,Q,K 21.47% -16.8%
A 11.62% -15.9%

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