The Math Behind the Calculator

How Multi-Hand Variance Works

In multi-hand video poker, all N hands share the same initial deal. You choose which cards to hold, and each hand receives its own independent draw. This correlation on the hold decision means the variance per deal scales approximately as N × single-hand variance — more than single-hand, but less than N independent games.

Expected Value

EV per deal = N × bet × (RTP − 1)
Total EV = sessions × deals × EV per deal

Standard Deviation

σ per deal = bet × √(N × variance)
σ per session = σ_deal × √(deals_per_session)

Risk of Ruin

RoR = e^(2 × bankroll × edge / σ²_deal)
edge = N × bet × (RTP − 1)

Same Game, Completely Different Risk

Hands Bet/Hand Cost/Deal Std Dev/Deal Deals/Hour Bankroll Needed
1 hand $1.25 $1.25 $5.51 ~600 $200
5 hands $0.25 $1.25 $12.34 ~500 $600
10 hands $0.25 $2.50 $17.45 ~450 $1,200
50 hands $0.25 $12.50 $39.05 ~400 $5,000
100 hands $0.25 $25.00 $55.22 ~350 $9,000

* All 9/6 Jacks or Better. "Bankroll Needed" is approximate figure for 95% chance of surviving 20 sessions.

⚠ Important Disclaimer

This calculator uses mathematical approximations. Actual outcomes will vary. The risk of ruin formula assumes continuous play with no table limits. This tool is for educational purposes only. Always set a strict loss limit and never gamble with money you cannot afford to lose.

Optimal Strategy Charts

Once you know your risk profile, use these strategy charts to play each game perfectly and maximize your expected return.