Probability

How to calculate Shoot the Gate probability

Count goal, post and outside outcomes in a standard deck without replacement.

Updated 2026-09-20

This guide uses testable rule assumptions and does not infer any platform’s implementation from its name. It is educational material, not betting advice.

Key definition

After two distinct ranks are exposed, 50 cards remain, so the conditional-probability denominator is 50.

How to verify it

If g ranks lie between the boundaries, there are usually 4g goal cards. Three matching cards remain at each boundary, making six post cards.

P(goal | endpoints) = 4g / 50
P(post | endpoints) = 6 / 50
P(outside | endpoints) = (44 - 4g) / 50

Limits and conclusion

Outside cards equal 50−4g−6. The three counts must sum to 50 as a basic check.

Practical checklist

For 5 and 9, g=3: goal 12/50, post 6/50 and outside 32/50. This result only fits the stated rules.

Practical checklist

  • After two distinct ranks are exposed, 50 cards remain, so the conditional-probability denominator is 50.
  • Outside cards equal 50−4g−6. The three counts must sum to 50 as a basic check.
  • Fix the rules, preserve a complete record, separate training from testing, and only then ask whether a model adds information beyond a simple baseline.