Ok so this is niche. I have a soft spot for probability games - the kind synonymous with casinos, where the rules fit on a napkin but the strategy doesn't. Flip7 scratched that itch for me.
My strategy of playing wreckless was entertaining for everyone except my point total and I became curious what GTO play would be like. Not to have a secret weapon for winning or anything, I still play dumb for fun, but just as a mental exercise.
So, as any reasonably sane person would do: I ran 240,000 simulations.
The Game
For the uninitiated, Flip7 works like this:
The deck is triangular. One 0, one 1, two 2s, three 3s... all the way up to twelve 12s. Plus 12 special cards (+2, x2, freeze, etc). That's 79 number cards total.
Each round, you draw cards from a face-down deck. After each draw, you choose: draw again, or bank your points and end the round. If you draw a duplicate of something already in your hand, you bust - zero points, round over.
The hook: if you collect 7 unique cards without busting, you get a +15 point bonus on top of whatever you scored. First to 200 wins.
# The deck composition that will haunt your decisions
deck = [0] + [i for i in range(1, 13) for _ in range(i)]
# [0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ...]The cards are face-up once drawn, so you could count cards and calculate exact probabilities. But I was more interested in GTO play - what's the baseline optimal strategy before you start adjusting for table dynamics?
How I Actually Played (Badly)
My gut said bank around 20-30 points. Since higher numbers appear more frequently, you'll probabilistically draw bigger cards - something like 12, 10, 8 felt common. Three or four turns, bank, repeat.
If I had a "second chance" card, I'd ride it until I lost the protection, then bank if I'd been drawing for a while. Standard stuff.
When I drew a run of small cards (0, 2, 3), I'd keep going because surely a big card was coming. When I was behind on points, I'd play "looser" - more draws, more risk. When ahead, I'd tighten up.
This all felt logical.
The Math (Where It Gets Interesting)
Let's start with some napkin probability.
You draw a 12. What's the probability you bust on the next draw? There are 11 other 12s in a 78-card remaining deck: 11/78 ≈ 14.1%.
Not bad. But what about after a few more draws?
| Cards in Hand | Worst-Case Bust Probability |
|---|---|
| 2 cards | ~9% |
| 3 cards | ~27% |
| 4 cards | ~40% |
| 5 cards | ~51% |
| 6 cards | ~60% |
By the 5th card, you're flipping a coin on survival. And yet there I was, drawing for that sweet +15 bonus like it was free money.
The expected value of a single random draw is about 8.2 points (weighted by deck composition). So in theory, a "safe" single-card strategy should average 8 points per round. But we can do better - the question is how much better, and at what risk.
This is where simulation beats napkin math.
The Simulation
I built a Monte Carlo simulation to test different stopping strategies. 10,000 games each, tracking:
- Avg Points/Round - efficiency
- % Round Bust - risk
- Game Win Rate - does it reliably hit 200 within 30 rounds?
- Avg Rounds to Win - speed
The strategies fall into three categories: stop after N cards, stop after N high cards, or stop at N points.
Strategy 1: Card Counting
The simplest approach. Draw exactly N cards, then bank.
3 cards is the sweet spot. 17.64 points per round with a 26% bust rate and 100% game win rate.
The "go big or go home" strategy - drawing until you hit 7 cards or bust - is catastrophic. 91% bust rate. 5.73 points per round. 36% game win rate.
That +15 bonus isn't free money. It's a trap.| Strategy | Pts/Round | Bust % | Game Win % | Rounds to Win |
|---|---|---|---|---|
| 1 card | 8.24 | 0.0% | 99.98% | 24.78 |
| 2 cards | 14.70 | 9.3% | 100% | 14.16 |
| 3 cards | 17.64 | 26.2% | 100% | 12.02 |
| 4 cards | 16.85 | 46.1% | 99.96% | 12.82 |
| 5 cards | 13.08 | 65.8% | 97.69% | 16.81 |
| 6 cards | 8.44 | 81.2% | 69.32% | 23.73 |
| 7 cards | 5.73 | 91.4% | 36.40% | 26.66 |
Notice how 4 cards is worse than 3 cards for points per round? The bust rate nearly doubles (26% → 46%) but you're not compensated with proportionally more points. Diminishing returns kick in hard.
Strategy 2: High Card Triggers
Here's a smarter approach. Instead of counting cards, count dangerous cards.
High cards (9, 10, 11, 12) have more duplicates in the deck. A 12 has 11 other copies lurking. A 2 only has one. So holding high cards is riskier than holding low cards.
The strategy: stop after drawing N high cards (9 or above).
| Strategy | Pts/Round | Bust % | Game Win % | Avg Cards Drawn |
|---|---|---|---|---|
| Single high | 13.22 | 6.6% | 100% | 1.74 |
| Double high | 17.74 | 36.0% | 100% | 3.29 |
| Triple high | 12.62 | 70.2% | 95.55% | 4.29 |
Double high slightly beats "stop at 3 cards" - 17.74 vs 17.64 points per round.
The elegance is that it's adaptive. Sometimes you stop at 2 cards (if both are 10+), sometimes at 5 cards (if you keep drawing 3s and 4s). It naturally adjusts risk based on hand composition.
This is closer to how good players intuitively play - they're not counting cards, they're feeling the danger level of their hand.
Strategy 3: Point Thresholds
But we can do better still. What if we stop when we hit a target point value?
First, a broad sweep:
| Threshold | Pts/Round | Bust % | Game Win % |
|---|---|---|---|
| 10 pts | 12.95 | 4.3% | 100% |
| 15 pts | 16.61 | 13.3% | 100% |
| 20 pts | 18.23 | 23.5% | 100% |
| 25 pts | 18.34 | 36.5% | 100% |
| 30 pts | 17.20 | 48.9% | 99.97% |
| 35 pts | 14.67 | 62.2% | 98.92% |
The sweet spot is somewhere between 20-25 points. Let's zoom in:
22-23 points is optimal. 18.5 points per round, 100% game win rate, ~11.5 rounds to victory.
| Threshold | Pts/Round | Bust % | Rounds to Win |
|---|---|---|---|
| 20 pts | 18.23 | 23.5% | 11.62 |
| 21 pts | 18.40 | 25.8% | 11.54 |
| 22 pts | 18.48 | 28.9% | 11.46 |
| 23 pts | 18.52 | 31.3% | 11.55 |
| 24 pts | 18.37 | 34.6% | 11.71 |
| 25 pts | 18.34 | 36.5% | 11.61 |
The difference between 22 and 23 is negligible - both are effectively optimal. Pick whichever is easier to track in your head.
The Final Rankings
After 240,000 simulated games:
Tier S: Optimal
- Stop at 22-23 points: 18.5 pts/round, ~11.5 rounds to win, 100% win rate
Tier A: Excellent
- Double high: 17.74 pts/round (adaptive, easy to feel)
- Stop at 3 cards: 17.64 pts/round (simple, reliable)
Tier B: Fine
- Stop at 20-21 points
- Stop at 4 cards
Tier F: Don't
- Stop at 6+ cards
- "Go big or go home" (91% bust rate, 36% win rate)
What surprised me
The biggest surprise was the 7-card bonus. +15 points feels significant. But the math is brutal:
- Probability of hitting 7 cards: ~8.7%
- Expected value of going for 7: 5.73 pts/round
- Expected value of stopping at 3: 17.64 pts/round
The bonus would need to be +80 points to make "go big or go home" competitive. At +15, it's a sucker bet, but feels good when you hit.
And playing "loose" when behind? Mathematically, you should play the same strategy regardless of score. The cards don't know you're losing. If anything, desperation draws just accelerate your loss.
What I Didn't Test
I purposely ignored the special cards in the deck (freeze, second chance, flip 3 and the extra points.) I wouldn't count them as insignificant, but these are the extra variants that even the playing field on probabilities, and make the game more fun, like the special cards in Uno. I also didn't model multiple players. The logic behind how different players play and probabilities are interesting too for sure, but maybe one for a future extension.
All simulations run with 10,000 games per strategy, 30-round max, 200-point target.