Calculating Poker Pot Odds with Ujogo
Pot Odds Overview
Poker players use pot odds to determine the expected value (profitability over the long run) of a play. In general, poker odds may be expressed as a win-to-loss ratio. Odds may be converted into percentage probabilities using the formula: win / (win + loss) %. The most straightforward explanation of how to calculate poker pot odds is to compare the total number of unknown cards to how many outs (unseen cards that could make your hand a winner) you have, and then do some simple division.
For every potential action (check, fold, call, raise) at every point in a game of poker, the mathematically correct strategy is influenced by the pot odds facing the poker player (and offered to the opponent(s)). The higher the pot odds facing a call, the more likely it is that calling is the correct play. The lower the poker pot odds facing a call, the more likely it is that folding will be the correct play.
Simple Poker Pot Odds
Simple pot odds, or "expressed pot odds", apply when considering calling a bet. Simple poker pot odds are the ratio of the size of the potential bet to the size of the pot (bet-to-pot ratio).
Example: If a poker player is holding Ac and 5c, and the 4 community cards are Jc, 3c, 7s, Kh, then this player can win the hand only when another club appears on the river. (Let's assume for simplicity-sake that an A on the river will not help our player.) This means that our poker player can only win if any one of the remaining 9 clubs shows up. Our player only has information about 6 cards at this point, his two hole cards and the four community cards. Thus, there are 46 cards that he hasn't seen (52 minus 6). What this also means is that 37 of the remaining cards (the non-clubs) will NOT help our player. Our poker player's odds are 37/9, or more simply, 4.1 to 1 odds against making his draw. So, the mathematically correct play here is to only call a bet if there is already at least 4.1x that amount of the call already in the pot.
So if you were playing a poker game of $5/$10 limit, then there would need to be at least $41 already in the pot to justify your calling a $10 bet to see the last card. Our poker player would need to call $10 to win the $51 that is now in the pot. That's approximately 1:5, or 20%. Therefore, a player should call a bet if his probability of winning is greater than the amount of the bet divided by the sum of the pot plus the bet [bet / (pot size + bet)]. An abbreviated way to estimate your simple poker odds percentage for one card remaining is to multiply the number of outs (9 in this example) by 2, and then add 2. That's 20%, which is very often going to match the math used above.
In our example, if there were two community cards remaining, not just the river, then a simple method for calculating our poker player's chance of winning, and thus his pot poker odds, can be achieved by simply multiplying the total number of outs by 4. This means that our poker player has about a 36% (4 x 9) chance of winning this hand with two community cards left to be showing.
Manipulating Poker Pot Odds
Often a poker player will bet to manipulate the pot odds offered to other players. A common example of manipulating poker pot odds is making a bet to protect a made hand that discourages opponents from chasing a drawing hand.
