| High Side Improvement Odds | ||||
| Drawing Two Cards to Selected 5th Street Hands | ||||
| 5th Hand | Example | Improve To | % | Approx. Odds Against |
| Pair | Q Q 3 5 10 | 2 Pair | 32.50% | 2 to 1 |
| Trips | 6.70% | 14 to 1 | ||
| Full House | 2.50% | 39 to 1 | ||
| Quads | 0.10% | 1000 to 1 | ||
| 2 Pair or Better | 41.70% | 1.5 to 1 | ||
| Two Pair | Q Q 3 3 10 | Full House | 15% | 5.5 to 1 |
| Quads | 0.20% | 500 to 1 | ||
| Full House or Better | 15.30% | 5.5 to 1 | ||
| Trips | Q Q Q 3 5 | Full House | 24.40% | 3 to 1 |
| Quads | 4.30% | 22 to 1 | ||
| Full House or Better | 28.80% | 2.5 to 1 | ||
| 4 Card Open End Straight | 3 8 9 10 J | Straight | 31.80% | 2 to 1 |
| 4 Card Straight with Ace | 5 J Q K A A 2 3 4 8 |
Straight | 15.90% | 5.5 to 1 |
| 4 Card Inside Straight | 2 8 9 J Q | Straight | 15.90% | 5.5 to 1 |
| 3 Card Open End Straight | 2 4 9 10 J | Straight | 4.40% | 22 to 1 |
| 4 Card Flush | 2d 5s 7s 10s Js | Flush | 38.30% | 1.5 to 1 |
| 3 Card Flush | 4c 7d 9h Kh Ah | Flush | 4.20% | 23 to 1 |
| 4 Card Open End Straight Flush | 3h 8s 9s 10s Js | Flush | 28.50% | 2.5 to 1 |
| Straight | 23.30% | 3.5 to 1 | ||
| Straight Flush | 8.30% | 11 to 1 | ||
| Straight or Better | 60.10% | .7 to 1 | ||
| 3 Card Open End Straight Flush | 2s 5c 9d 10d Jd | Flush | 3.90% | 29 to 1 |
| Straight | 4.20% | 23 to 1 | ||
| Straight Flush | 0.28% | 356 to 1 | ||
| Straight or Better | 8.30% | 11 to 1 | ||
| Low Side Improvement Odds | ||||
| Drawing Two Cards to Selected 5th Street Hands | ||||
| 5th Hand | Example | Improve To | % | Approx. Odds Against |
| 4 Card 8 Low | 3 5 7 8 J | 8 Low | 46% | 1.2 to 1 |
| Lower Than 8 Low | 9% | 10 to 1 | ||
| Any Low | 55% | .8 to 1 | ||
| 4 Card 7 Low | A 2 6 7 9 | 7 Low | 50% | 1 to 1 |
| Lower Than 7 Low | 5% | 19 to 1 | ||
| Any Low | 55% | .8 to 1 | ||
| 4 Card 6 Low | A 3 4 6 Q | 6 Low | 53% | 1 to 1 |
| Lower Than 6 Low | 1.50% | 65 to 1 | ||
| Any Low | 55% | .8 to 1 | ||
| 4 Card 5 Low | A 2 4 5 10 | 5 Low | 16% | 5 to 1 |
| Any Low | 55% | .8 to 1 | ||
| Any 3 Cards to a Low | 2 4 7 9 K | Any Low Hand | 15% | 6 to 1 |
| # | % of 56 | |
| 5 low | 1 | 1.80% |
| 6 low | 5 | 8.90% |
| 7 low | 15 | 26.80% |
| 8 low | 35 | 62.50% |
| Total | 56 | 100% |
| Hand | Frequency | Probability | Cumulative | Odds |
|---|---|---|---|---|
| Royal flush | 4,324 | 0.0032% | 0.0032% | 30,939 : 1 |
| Straight flush | 37,260 | 0.0279% | 0.0311% | 3,216 : 1 |
| Four of a kind | 224,848 | 0.168% | 0.199% | 594 : 1 |
| Full house | 3,473,184 | 2.60% | 2.80% | 37.5 : 1 |
| Flush | 4,047,644 | 3.03% | 5.82% | 32.1 : 1 |
| Straight | 6,180,020 | 4.62% | 10.4% | 20.6 : 1 |
| Three of a kind | 6,461,620 | 4.83% | 15.3% | 19.7 : 1 |
| Two pair | 31,433,400 | 23.5% | 38.8% | 3.26 : 1 |
| One pair | 58,627,800 | 43.8% | 82.6% | 1.28 : 1 |
| No pair | 23,294,460 | 17.4% | 100% | 4.74 : 1 |
| Total | 133,784,560 | 100% | 100% | 0 : 1 |
| Hand | Frequency | Probability | Cumulative | Odds |
|---|---|---|---|---|
| 5-high | 781,824 | 0.584% | 0.584% | 170.12 : 1 |
| 6-high | 3,151,360 | 2.36% | 2.94% | 41.45 : 1 |
| 7-high | 7,426,560 | 5.55% | 8.49% | 17.01 : 1 |
| 8-high | 13,171,200 | 9.85% | 18.3% | 9.16 : 1 |
| 9-high | 19,174,400 | 14.3% | 32.7% | 5.98 : 1 |
| 10-high | 23,675,904 | 17.7% | 50.4% | 4.65 : 1 |
| Jack-high | 24,837,120 | 18.6% | 68.9% | 4.39 : 1 |
| Queen-high | 21,457,920 | 16.0% | 85.0% | 5.23 : 1 |
| King-high | 13,939,200 | 10.4% | 95.4% | 8.60 : 1 |
| Total | 127,615,488 | 95.4% | 95.4% | 0.05 : 1 |
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