We're about to enter to the part of mathematical world that you certainly must know about. All the bigger winners are familiar with these concepts, and they have found ways to make them even more advanced. I will elaborate on this subject in future articles, but here's information for players who aren't familiar with these concepts yet.
Pot Odds Introduction
Pot odds will take you to where mathematical knowledge really matters. However, without knowing stuff about your opponent and his hand it's hard to take an advantage of pot odds. The better you know your opponent, the more you'll be able to come up with correct calculations and profitable plays. You'll need to know what kind of chances you've got to win, and in order to know this, you have to know your opponent's hand range and his way of thinking.
This also explains why players without great mathematical abilities can win at poker - they make their own calculations, not in numbers on a paper, but by knowing enough about their opponents, understanding the psychological side of poker well enough so that they can come up with correct assumptions often enough. While people who are great at math can come up with different kinds of calculations but find no real help in them since they don't understand poker and/or their opponents.
Do we get positive pot odds to call? Or positive pot odds to bet? Two things matter; the cost of the call/bet and the size of the pot. If we're to call a $20 bet and pot is $40, we'll risk $20 in order to win $80 ($40 in the pot, $20 from you and $20 from your opponent) - meaning 3 : 1 pot odds. When we know our odds, we sum those odds up with each other like following shows: 3 + 1 = 4. And now, we divide 1 by 4 (since we risked 1 out of 4 to the pot) and this naturally gives us 25%. We risk money worth of 25% of the pot, and this means our probability to improve to a winning hand must be bigger than 25% to justify our call.
Having a flush draw on turn means 19.6% chance to improve to a flush. We're on the negative side, not much though, but this wouldn't give us correct pot odds to call since this doesn't look like a positive play. We can however think this through again by using other kind of odds and an improved way of thinking. Anyway, now you're familiar with the concept of pot odds - it's just about the amount you risk and the size of the pot versus how likely it is that you'll make winning hand.
Just to beat this point home, if our opponent had only bet $10 to a $40 pot, it would be correct to call here since $10 (our bet) + $10 (opponent's bet) + $40 (pot) = $60. Then 10/60 = 0.167 = $16.7. Obviously, our 19.1% probability would make this call profitable, since our draw is close to 4 : 1 and pot odds are 5 : 1.
Probabilities for Pot Odds Calculations:
Flush Draw: 9 Outs
Open-ended Straight Draw: 8 Outs
Gutshot Straight Draw: 4 Outs
| Outs |
Turn Hit % |
River Hit % |
Turn + River Hit % |
| 1 |
2.1 |
2.2 |
4.3 |
| 2 |
4.3 |
4.3 |
8.4 |
| 3 |
6.4 |
6.5 |
12.5 |
| 4 |
8.5 |
8.7 |
16.5 |
| 5 |
10.6 |
10.9 |
20.4 |
| 6 |
12.8 |
13 |
24.1 |
| 7 |
14.9 |
15.2 |
27.8 |
| 8 |
17 |
17.4 |
31.5 |
| 9 |
19.1 |
19.6 |
35 |
| 10 |
21.3 |
21.7 |
38.4 |
| 11 |
23.4 |
23.9 |
41.7 |
| 12 |
25.5 |
26.1 |
45 |
Poker Mathematics:
Poker Probability,
Pot Odds
(Continue: Implied Odds),
Expected Value,
Winnings in the Long Run
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