ポーカーオッドと確率：どんなプレイヤーに必要な数学
The Mathematics of Poker
Poker is a game of incomplete information, but the mathematics behind it are precise. Understanding poker math lets you make decisions based on expected value rather than intuition.
Basic Probability: The Deck
A standard deck has 52 cards: 13 ranks in 4 suits. Before the flop in Hold'em, you have 2 cards from 52. The probability of getting a specific hand is calculated by counting combinations.
Common Preflop Probabilities
- AA or KK: 1.1% (about 1 in 110)
- Any pocket pair: 5.9% (about 1 in 17)
- AK suited: 0.3% (about 1 in 331)
- AK offsuit: 0.9% (about 1 in 110)
Pot Odds
Pot odds are the ratio of the current pot size to the cost of a call. They tell you the minimum equity you need to call profitably.
Formula: Pot Odds = Cost to Call / (Pot + Cost to Call)
Example: Pot is $100, opponent bets $50. Call $50 to win $150. Pot odds = 50/150 = 33%
The Rule of 2 and 4
Quick equity estimation for drawing hands:
- Multiply outs by 2 for one card to come
- Multiply outs by 4 for two cards to come
- Example: 9 outs on flop = 18% (turn) or 36% (river)
Implied Odds
Implied odds extend pot odds by considering future betting rounds. When you hit your draw, how much more can you win?
Formula: Implied Odds = (Current Pot + Future Expected Bets) / Current Cost to Call
Expected Value
EV is the average result of a decision if repeated infinitely. Calculate EV by multiplying each outcome by its probability and summing.
Example: 40% chance to win $200 = $80 EV