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3.2 Poker Math - Texas Holdem Pot Odds continued...
Texas Holdem Pot Odds
When we calculate the Pot Odds we are simply looking to see how much money we will win in return for the amount of our bet.
It’s a very simple calculation
| Pot Odds = Total Pot divided by the Bet I would have to call |
Illustration
Small Blind 5 cents
Big Blind 10 cents
You are in the big blind. Before the flop everyone folds round to the small blind who calls the extra 5c. Total pot before the Flop is therefore 20cents.
After the flop the small blind bets 10c, what are the pot odds?
Total Pot = 20cents + 10 cents bet = 30 cents
Total Bet I would have to make = 10 cents
Therefore the pot odds are 30 cents divided by 10 cents or 3 to 1.
What does this mean? It means that in order to break even we would need to win Once for every 3 times we lose. The amount we would win would be the Total Pot + the bet we make = 30 cents + 10 cents = 40 cents.
| Bet number | Outcome | Stake | Winnings |
| 1 | LOSE | 10 cents | Nil |
| 2 | LOSE | 10 cents | Nil |
| 3 | LOSE | 10 cents | Nil |
| 4 | WIN | 10 cents | 40 cents |
| TOTAL | BREAKEVEN | 40 cents | 40 cents |
Break Even Percentage
Now we need to convert this into a Break Even Percentage.
| Break Even Percentage = 100% divided by (Pot odds added together) |
Let me explain a bit further. Pot Odds added together means replace the “to” with a plus sign eg: 3 to 1 becomes 3+1 = 4
So in the example above our pot odds are 3 to 1 so our Break Even Percentage = 100% divided by 4 = 25%
Note - This only works if you express your pot odds against a factor of 1 eg: "3 to 1" or "5 to 1" etc. It will not work if you express the pot odds as any other factor eg: 3 to 2 etc.
Making a Decision
So lets bring the two elements together and arrive at a decision.
To do this we compare the percentage probability that we are going to hit one of our Outs and win the hand, with the Break Even Percentage.
Using the two examples above (assuming they are the same hand)
Probability of Hitting an Out = 48%
Break Even Percentage = 25%
If our Probability of hitting an out is higher than the Break Even percentage then this represents a good bet – the odds are in our favour.
Why? Because what we are saying above is that we are going to get the winning hand 48% of the time, yet in order to break even we only need to hit the winning hand 25% of the time, so over the long run making this bet will be profitable.
Hand Walkthrough
Lets take this opportunity to see how Poker Math works in a hand walkthrough
| Small Blind | 5 cents |
| Big Blind | 10 cents |
| Your Position | Big Blind |
| Your Hand | K 10 |
| Action to you | Everyone folds to the dealer who calls and the small blind calls |
Two people have called and per the Starting hand chart you should just check here, so the Total Pot before the flop = 30 cents.
Flop comes down Q
J
6
and the Dealer bets 10c, the small blind folds.
Do we call? Lets go through the thought process:
How has the Flop helped my hand? - It hasn’t but we do have some draws as we have an open ended straight draw (any Ace or 9 will give us a straight) We also have an overcard with the King.
How has the Flop helped my opponent? - The Dealer did not raise before the flop so it is unlikely he is holding a really strong hand. He may have limped in with high cards or suited connectors. At this stage our best guess is to assume that he has hit top pair and holds a pair of Queens. It’s possible that he hit 2 pair with Q J or he holds a small pair like 6’s and now has a set, but we come to the conclusion that this is unlikely.
How many Outs do we have? - So we conclude that we are facing top pair, in which case we need to hit our straight or a King to make top pair.
Open Ended Straight Draw = 8 Outs (4 Aces and 4 Nines)
King Top Pair = 3 Outs (4 Kings less the King in our hand)
Total Outs = 11 Probability of Winning = 11 x 4 = 44%
What are the Pot Odds? - Total Pot is now 40 cents and we are asked to call 10 cents so our Pot odds are 4 to 1 and our break even % = 100% divided by 5 = 20%.
So now we have quickly run the numbers it is clear that this is a good bet for us (44% vs 20%), and we make the call – Total Pot now equals 50 cents.
Turn Card = 3 and the dealer makes a bet of 25 cents
After the Turn Card - This card has not helped us and it is unlikely that it has helped our opponent, so at this point we still estimate that our opponent is in the lead with top pair.
We still need to hit one of our 11 Outs and now with only the River card to come our Probability of Winning is now = 11 x 2 = 22%
The Total Pot is now 75 cents and our Pot odds are 75 divided by 25 = 3 to 1. This makes our Break Even percentage = 100% divided by 4 = 25%
So now we have the situation where our probability of winning is less than the break even percentage and so at this point we would fold, even though it is a close call.
CONTINUE TO NEXT SECTION - 3.3 - Poker Challenge *Stage 3* $29 - $32
