Up date of what I think I learned regarding pot odds and breaking even

Lets look at 4:1 odds to see if we can determine where we break even. First, what this means is if you put in 1 you are getting 5 back in return (you'll net 4, but you get back 5 which includes the 1 you put in.). Lets just look at one event where you win. You put in 1 and get back 5. Simple, right.

Lets expand this to two events, win one lose one. We already know when you win you pay 1 and get 5 back. In the second event you pay 1 and get nothing. Now lets combine the two events: You paid 2 and got back 5.

Three events: win one, lose two. This results in paying 3 and getting back 5.

So far in all these event you are ahead as the payout of 5 has exceeded the amounts you put in.

What about Four events: Win one, lose 3. We get 5 and we put in 4. Still ahead

Five events : win one, lose four. Put in 5 and get 5 back. Let me repeat that - Put in 5 and get 5. Looks like we've reached out break even point. It's not a coincidence. The break even point IS EQUAL to the odds. 4:1 pots odds means lose 4 times:win once. This is the break even point.

What if you want to convert our 4:1 odds to a percent. Or to rephrase the question; How often do I need to win if the pot is offering me 4:1 odds. The answer is NOT 1/4 for 25%. 1/4 means I won once out of four events. Four is a specific set of outcomes, the bad ones, not the total. For percents we wnat the total outcomes. (See More info below) As we've discovered above it takes a total of 5 events, of which winning one, gets us to a break even point. Winning one out of 5 is 20%.

Remember odds are the two outcomes of an event expressed againt each other. Lets use a simple coin flip. Heads or tails -whats the odds? 1:1. It's either heads or tails.

What about percent. Also refered to as chance. What's the chance of me flipping a coin and getting heads? Odds are 1:1. Can we divide 1/1? Well that gives us 1? Is that 100% then? Obviously not. We can no more divide 1/1 now, than we could divide 4/1 earlier. Percent is the relationship of a specific outcome occuring to the total outcomes possible in an event. Flipping the coin is the event. It has two possible outcomes - heads or tails. If we compare the specific outcome of heads to the total outcomes we get 1 to 2, or 50%

Converting 4:1 odds to percent we need to apply the same principles we used when flipping the coin. 4 is the number of bad outcomes and 1 is the number of good outcomes (review my odds definition two paragraphs above if this doesn't make sense). Bad outcomes plus good outcomes equal total outcomes. So 4+1 =5. We get 5 total outcomes of which 1 is good. 1/5=20%. To use Phils math equation I would get 1/(4+1) or 1/5. The +1 is just getting the denominator to equal total outcomes, rather than just one specific set of outcomes.

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