Kansas City Lowball · fixed limit · three draws

2-7 Triple Draw Cheat Sheet

Every number worth knowing before you post a blind: exact dealing odds, what the table is likely holding against you, and all 154 playable starting-hand shapes ranked by how often they actually win a showdown.

aces are always high straights & flushes count against you the nuts is 7-5-4-3-2 wheel cards: 2 3 4 5 7 X = any ten or higher

What you’ll be dealt

Exact odds — every one of the 2,598,960 possible five-card hands enumerated.

34.1%

dealt at least one deuce — the card every good hand needs

49.3%

at least one pair — half your deals start damaged

4.75%

pat T-low or better off the deal

0.039%

the dealt nuts, 7-5-4-3-2 — once per ~2,550 hands

Holding off the deal	Odds	Holding off the deal	Odds
deuce + 1 more wheel card (3 4 5 7)	27.36%	pat T-low or better	4.75%
deuce + 2 more wheel cards	11.14%	pat 9-low or better	2.04%
deuce + 3 more wheel cards	1.54%	pat 8-low or better	0.71%
any 2 distinct wheel ranks	58.47%	pat 7-low	0.16%
any 3 distinct wheel ranks	17.91%	3 distinct ranks 2–8	45.11%
any 4 distinct wheel ranks	1.91%	4 distinct ranks 2–8	11.17%
all 5 wheel ranks dealt	0.04%	dealt straight or flush	0.55%

What the table holds against you

200,000 simulated deals per table size, card removal honored. A “premium start” here is three or more wheel cards.

Opponents	≥1 pat T-low	≥1 premium start	≥1 strong one-card draw*	How many premium starts out there
1	4.7%	17.8%	11.1%	none 82% · one 18%
2	9.2%	33.2%	21.3%	none 67% · one 31% · both 2.6%
3	13.9%	46.5%	30.8%	none 53% · one 39% · two 7% · three 0.3%
4	17.8%	57.1%	38.9%	none 43% · one 44% · two 12% · 3+ 1.1%
5	21.9%	66.2%	46.6%	none 34% · one 46% · two 18% · 3+ 2.6%

At a full 6-max table, two out of three deals put a premium start in someone else’s hand — and about one deal in five has a pat T-low already made behind you.

*four distinct ranks 8 or lower — a one-card draw at an 8-low shell.

Should you stand pat?

Second draw is done: you’re in position and everyone drawing missed. If you stand pat, these are the exact odds you get outdrawn on the final draw. Heads Up: one opponent on the listed draw, outs over 43 unseen cards. Vs. 2 Opponents: both opponents hold the listed draw type and each catches one card — the odds at least one gets there.

You stand pat with	vs 7-4-3-2 (smooth 7, deuce)	vs 8-5-4-2 (8 draw)	vs 2-3-4-5 (wheel cards)
9-7-4-3-2	27.9%12 outs: 5·6·8	23.3%10 outs: 3·6·7	23.3%10 outs: 7·8·9
9-6-4-3-2	25.6%11 outs: 5·6·8	23.3%10 outs: 3·6·7	25.6%11 outs: 7·8·9
9-5-4-3-2	25.6%11 outs: 5·6·8	25.6%11 outs: 3·6·7	18.6%8 outs: 7·8
8-7-4-3-2	18.6%8 outs: 5·6	16.3%7 outs: 3·6	14.0%6 outs: 7·8
8-6-4-3-2	16.3%7 outs: 5·6	7.0%3 outs: 3	16.3%7 outs: 7·8
8-5-4-3-2	16.3%7 outs: 5·6	0 outschop only	9.3%4 outs: 7
7-6-4-3-2	9.3%4 outs: 5	drawing dead	7.0%3 outs: 7

You stand pat with	vs 7-4-3-2 (smooth 7, deuce)	vs 8-5-4-2 (8 draw)	vs 2-3-4-5 (wheel cards)
9-7-4-3-2	52.6%both get there: 8.9%	45.2%both get there: 6.1%	45.2%both get there: 6.1%
9-6-4-3-2	49.0%both get there: 7.4%	45.2%both get there: 6.1%	49.0%both get there: 7.4%
9-5-4-3-2	49.0%both get there: 7.4%	49.0%both get there: 7.4%	37.2%both get there: 3.8%
8-7-4-3-2	37.2%both get there: 3.8%	33.1%both get there: 2.8%	28.7%both get there: 2.0%
8-6-4-3-2	33.1%both get there: 2.8%	15.0%both get there: 0.4%	33.1%both get there: 2.8%
8-5-4-3-2	33.1%both get there: 2.8%	0 outschop only	19.7%both get there: 0.8%
7-6-4-3-2	19.7%both get there: 0.8%	drawing dead	15.0%both get there: 0.4%

Even your roughest pat is a big favorite heads-up: a pat 9-7 loses to a live one-card draw only 23–28% of the time. The sneaky column is 2-3-4-5 — it can’t catch a 6 (straight), so its winning cards are 7s, 8s and 9s: it threatens a pat 8-6 (16.3%) more than a smooth 8-draw does (7.0%). Note the zeros: 8-5-4-3-2 can’t be beaten by the 8-5-4-2 draw at all. But add a second live draw and the rough pats get uncomfortable — a pat 9-7 against two smooth 7-draws is a coin flip (52.6%), while a pat 7-6 still fades both more than 4 times in 5.

Winning catches are ranks; counts already account for every card you and the drawing hands block. Chops (identical hands) are not counted as outdraws. Exact enumeration — no simulation noise.

Every starting shape, ranked

All 154 two-, three-, and four-card classes (X = ten or higher), 10,000 showdowns each: you draw to the shape, everyone finishes all three draws against random hands. Toggle the table size from heads-up to 6-handed — at each size a random hand’s baseline is 100% divided by the players. Sorted by win rate; red rows are hands that can fill their own straight.

The straight traps are the sheet’s big lesson: 4567X is four babies and ranks 149th of 154 — a 6 or an 8 arrives disguised as help and hangs you. The gap between 2347X (73.0%) and 3457X (62.0%) is one card: the 3457 shape loses eleven points because a six fills 3-4-5-6-7. Add opponents and everything compresses toward the random baseline — 2347X drops from 73.0% heads-up to 61.4% 3-way and 49.3% 6-handed (still triple the 16.7% baseline), while the straight traps collapse to the very bottom: 789XX wins just 4.1% of 6-handed showdowns.

Method: hero’s first draw discards exactly the X cards; later draws follow the frozen rollout heuristic on both sides, no betting, ties split. 10k samples puts ±0.5pt of noise on each figure — adjacent ranks are interchangeable, tiers are not. Generated by the same engine that trained the app’s blueprints (verified bit-exact vs its Swift port).