The ruin of the player (close. gambler's ruin) means the loss of the last play capital and thus the possibility in gambling of further-passing on. Sometimes in addition the term designates the last, very high loss bet, which a player in hope platziert to recover all its past gambling losses.

In the game theory "“ruin of the player"” stands for the constantly sinking expectancy value of the play capital in the course of the play, if the profits are again invested.

Examples

We regard a with which everyone of the two players a chance has 50% to win one of the throws. After each throw the loser gives a cent to the winner. The play ends, if a player has no more money. If the number of the throws is unlimited, the probability for this playing amounts to 100%. If player possesses A n_1 cents and player B n_2 cents, the chances amount to P_1 and P_2 that player A and/or B without money ends:

P_1= \ frac {n_2} {n_1+n_2}

P_2= \ frac {n_1} {n_1+n_2}

Hence it follows that the player with the smaller starting capital will very probably lose. Even with same chances in detail throw will more probably win with increasing Spieldauer ever that player, who began with more cents.

However means this no positive expectancy value for rich players, because they lose with each lost play (many throws) more moneys than their poorer opponents. Assumed, two players with 90 and/or 10 cents repeat the entire play 100-mal. The player with 90 cents should win approximately 90 plays, 10 cents per play. It will lose in addition, approx. 10 plays and will lose dabe in each case 90 cents. At the end of the series it therefore won 90*10=900 cents and lost 10*90=900 cents. The expectancy value of both players after a large number of plays is the resembling and.

Casino plays

A typical casino play contains a small house advantage. This advantage is in the long-term anticipation value and can be expressed as portion of the assigned sum. It remains unchanged from play to play, rises however computationally with increasing Spieldauer, if it is referred to the starting capital of the player.

For example the official house advantage can be with a casino play 1%; the expectancy value for the disbursement for the player accordingly 99%. This calculation comes up, if the player would never use a gain to far plays. Idealized weather, which uses 100 euro, after the play 99 euro one kept. If it sets these 99 euro however again, it would lose on the average again 1% and would sink its expectancy value on 98,01 euro. The downward spiral continues to go, until the expectancy value approximates the zero: the ruin of the player.

The long-term anticipation value corresponds not necessarily to the result, which a certain player experiences. Players, who play a finite time long, can end with a net profit, regardless of the house advantage, or they can perish many faster than in the mathematical forecast.

A casino has usually

• "… many more moneys than each player, so that a player will many more probably suffer the "“ruin of the player"” than the casino;
• "… Chances of winning, which favour the casino and produce a negative expectancy value for the players;
• "… different risk strategies, which limit its maximum loss.

Thus it is secured that the casino in nearly all cases will win in the long term. A simulation of the "“ruin of the player:

Speculation

It can be shown that, where economic activities concentrate on the transmission of fortunes in place of on the structure of fortunes, which works ruin of the player with the result that most fortune is held by very few market participants. This becomes visible in the stock market, if speculative strategies outweigh in relation to long-term dividend-oriented investments.

See also

• Player false conclusion

Articles in category "Ruin of the player"

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