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The Difference Between "To" And "For" When Calculating Odds

A few things need to be said about the nature of odds, for this is one area the average thinks he or she knows about, but can be easily deceived, misled, or uniformed. But it represents a very fundamental difference for both the player, and not so inadvertently, the house.

When you see odds on roulette or craps or video poker, you may be thrown off by something that appears in the table in which the odds are explained. If you see that something pays off at 5 FOR 1, you might be thinking that if you have wagered $100, you are going to WIN $500, which, in the end, brings you back $600. Well, this is not true. When you bet $100 and you are getting "5 for 1" you are only getting $500, which includes the hundred dollars you originally bet.

When you bet $100 with odds of five TO one, your WIN total is $500, which is paid to you in addition to your original $100 bet.

Whenever you see 5 to 1, that means the PAYOFF is five times that of the wager. At 5 FOR 1, that means that for every dollar that is wagered, the player gets back five dollars.

Get it?

If not, here's a sample table, represented through a wager of $100:

----------------------------------------
WAGER: $100
xx .... For 1 .... To 1
10 .... $900 .... $1000
9 .... $800 .... $900
8 .... $700 .... $800
7 .... $600 .... $700
6 .... $500 .... $600
5 .... $400 .... $500
4 .... $300 .... $400
3 .... $200 .... $300
2 .... $100 .... $200
-----------------------------------------

As you can see, the wager we are operating off of is $100, and the numbers in the "To 1" column are consistently $100 less than those in the "For 1" column. This is something that often confuses a player, and in all honesty, it is not always something that is unintentional.

There is also some misinterpretation on the odds of various events happening. Even so-called "experts" make this mistake. But it means something, because there is a difference.

For example, there are 36 different combinations that can come out on a pair of dice in the game of craps. Six of those combinations add up to a total of seven. Of course, that means one out of every six combinations add up to 7. That's one IN six. That is NOT six to one. That is, in fact, 5 to 1. When we talk about six combinations appear out of 36, that means that thirty combinations DO NOT. Therefore, the ratio is 30 to 6. Now reduce it; divide each side by six and you come up with odds of 5 to 1.

Many people treat this in cavalier fashion, despite the fact that the outcomes expressed as percentages are actually quite different, and get even more pronounced as the samplings get smaller. You can see that illustrated by this table:

9 to 1 is 10% -- 1 in 9 is 11%
8 to 1 is 11% -- 1 in 8 is 12.5%
7 to 1 is 12.5% -- 1 in 7 is 14.3%
6 to 1 is 14.3% -- 1 in 6 is 16.7%
5 to 1 is 16.7% -- 1 in 5 is 20%
4 to 1 is 20% -- 1 in 4 is 25%
3 to 1 is 25% -- 1 in 3 is 33.3%
2 to 1 is 33.3% -- 1 in 2 is 50%