Does a Bad Player at the Table Cost You Money?
Updated
No. Not over any stretch of hands that matters. The player at third base who “took the dealer’s bust card” helps you exactly as often as they hurt you, and this is not a matter of opinion — it follows from a symmetry that can be stated in one paragraph.
- A bad player’s decisions do not change your expected value.
- They change which cards you get, not the distribution of cards you get.
- You notice the hands where it hurt. You do not notice the hands where it helped.
- They do hurt their own bankroll, and they do slow the game down.
The argument, in one paragraph
Before any card is dealt, the shoe is in some unknown order. Third base taking an extra card shifts every subsequent card one position along. Whether that shift helps or hurts you depends entirely on what the next card happens to be — and since the order is unknown and every arrangement is equally likely, the shift is as likely to hand you a good card as a bad one.
That is the whole proof. It requires no simulation, because it does not depend on how anybody plays. Any change in who receives which card, made without knowledge of the cards, leaves every player’s expectation exactly where it was.
Why it feels so wrong
Because the damage is visible and the benefit is invisible.
When third base hits a 15 against a dealer 6, draws the ten that would have busted the dealer, and the dealer then makes 20, you can point at the exact card and the exact person. When the same player hits a 15, draws a small card, and the dealer draws the ten they would otherwise have missed and busts — nobody says anything. The good outcome has no story attached to it.
This is the same reason people remember near-misses at slot machines and forget ordinary losses. The memory is selective, not the mathematics.
What a bad player does actually cost you
Three real things, none of which is your win rate.
Speed. A slow or indecisive player reduces hands per hour. If you have an edge, that costs you money; if you do not, it saves you some.
Cards seen. More players means more cards out per round, which is useful if you are counting and irrelevant otherwise.
Their own money. They are losing considerably more than you are. If they are a friend, the chart is free.
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By Martin Kosek · every number on this site is computed by us, not copied.
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