The math behind pair splitting
There are three different reasons to split a pair, which all result in lowering the house edge. The first reason is that profits over time will be maximized from hands that are in favour of winning. The second is that losses over time will be minimized for certain hands where the odds are against you. The third and last reason is that you’ll be able to turn some of the hands where the odds are against you into hands that in the long run will win. Let’s illustrate this by one example from each category.
Maximizing profits from winning hands
Let’s assume that you’re sitting at a table that is played with eight decks and where the rules state that it’s not allowed to double after a split. You’re being dealt 9 – 9, while the dealer is showing a 6. Your hand value of 18 is quite good against the dealer’s 6 as you on average will win 64% of the time if you decide to stand. Should you play this hand 100 times and bet €1 each time, you would on average make a net profit of €28. This is because 64 of your 100 hands would win and give you €64, while the remaining 36 hands would lose and lead to a loss of €36. The difference between these amounts is €28 (€64 – €36).
Even though this is profitable, you’ll on 100 hands on average be able to reach a net profit of €40 if you decide to split instead, which is €12 more. By splitting you’re actually lowering your chances of winning down to 60%, but as 60% is still in favour of winning the hand and you’re able to place an extra bet, this will generate a higher profit over time.
If you’re playing the hand 100 times, you’ll on average win 60 of them, which with a double stake will give you a profit of €120 (€2 * 60 won hands). The remaining 40 hands will become lost and with a double stake this will lead to a loss of €80 (€2 * 40 lost hands). This results in an average net profit of €40 (€120 – €80), which indeed is €12 more than the €28 you would have gotten if you chose to stand.
Minimizing losses from losing hands
Let’s assume that you’re still sitting at the same table with 8 decks in play, but this time you’re being dealt 7 – 7, whereas the dealer is showing a 2. Your hand value of 14 is not very good against this and therefore you’ll on average lose 64% of the hands, whereas you’ll win 36% of them. If you bet €1 on every hand and play a total of 100 hands, you’ll on average lose €28 (€64 – €36).
If you decide to split the hand you would get two hands with a value of 7. You would still be an underdog to win the hand, but you wouldn’t lose as often. On average you would lose 55% of your hands, whereas 45% of them would win. As you’re required to place an extra bet when you decide to split, you’re stake would be a total of €2. On the 100 hands played you would on average win €90 (€2 * 45 won hands) and lose €110 (€2 * 55 lost hands). This would result in a net loss of €20 (€90 – €110), which means that you on 100 played hands on average would lose €8 less by splitting.
Turning losing hands into winning ones
Once again let’s assume that you’re still sitting at the same table and that you once again were dealt 7 – 7, but that the dealer this time is showing a 6. Even if the dealer’s 6 is better for you than the 2 in the above example, you’ll still have the odds against you and lose money in the long run. On average you’ll win 42% of your hands and lose the remaining 58%. If you’re playing 100 hands with a stake of €1 each hand, you’ll on average lose €16 (€42 – €58).
By splitting your 7s you are however able to get an advantage in the hand as a 7 will win over the dealer’s 6 in the long run. By splitting you’ll on average win 52% of your hands and lose 48% of them. As you’re placing an extra stake when splitting, 100 hands will on average give you €104 (€2 * 52 won hands) and lose you €96 (€2 * 48 lost hands). This would result in a net profit of €8 (€104 – €96). By choosing to split your hand, you would in other words turn an average loss of €16 into a profit of €8.